diff --git a/guide/src/class/numeric.md b/guide/src/class/numeric.md
index 6f2e6e18..c6b6a65b 100644
--- a/guide/src/class/numeric.md
+++ b/guide/src/class/numeric.md
@@ -387,10 +387,10 @@ fn my_module(_py: Python<'_>, m: &PyModule) -> PyResult<()> {
 #
 # fn main() -> PyResult<()> {
 #     Python::with_gil(|py| -> PyResult<()> {
-#         let globals = PyModule::import(py, "__main__")?.dict();
+#         let globals = PyModule::import(py, "__main__")?.dict().as_borrowed();
 #         globals.set_item("Number", Number::type_object_bound(py))?;
 #
-#         py.run(SCRIPT, Some(globals), None)?;
+#         py.run_bound(SCRIPT, Some(&globals), None)?;
 #         Ok(())
 #     })
 # }
diff --git a/guide/src/module.md b/guide/src/module.md
index 9e52ab93..5d224de4 100644
--- a/guide/src/module.md
+++ b/guide/src/module.md
@@ -93,9 +93,9 @@ fn func() -> String {
 #    use pyo3::wrap_pymodule;
 #    use pyo3::types::IntoPyDict;
 #    let parent_module = wrap_pymodule!(parent_module)(py);
-#    let ctx = [("parent_module", parent_module)].into_py_dict(py);
+#    let ctx = [("parent_module", parent_module)].into_py_dict(py).as_borrowed();
 #
-#    py.run("assert parent_module.child_module.func() == 'func'", None, Some(&ctx)).unwrap();
+#    py.run_bound("assert parent_module.child_module.func() == 'func'", None, Some(&ctx)).unwrap();
 # })
 ```
 
diff --git a/guide/src/python_from_rust.md b/guide/src/python_from_rust.md
index 2f3be53a..753ce620 100644
--- a/guide/src/python_from_rust.md
+++ b/guide/src/python_from_rust.md
@@ -290,7 +290,7 @@ fn foo(_py: Python<'_>, foo_module: &PyModule) -> PyResult<()> {
 
 fn main() -> PyResult<()> {
     pyo3::append_to_inittab!(foo);
-    Python::with_gil(|py| Python::run(py, "import foo; foo.add_one(6)", None, None))
+    Python::with_gil(|py| Python::run_bound(py, "import foo; foo.add_one(6)", None, None))
 }
 ```
 
@@ -321,7 +321,7 @@ fn main() -> PyResult<()> {
         py_modules.set_item("foo", foo_module)?;
 
         // Now we can import + run our python code
-        Python::run(py, "import foo; foo.add_one(6)", None, None)
+        Python::run_bound(py, "import foo; foo.add_one(6)", None, None)
     })
 }
 ```
diff --git a/src/conversions/anyhow.rs b/src/conversions/anyhow.rs
index 3b5aa053..809b2aa2 100644
--- a/src/conversions/anyhow.rs
+++ b/src/conversions/anyhow.rs
@@ -147,8 +147,8 @@ mod test_anyhow {
         let pyerr = PyErr::from(err);
 
         Python::with_gil(|py| {
-            let locals = [("err", pyerr)].into_py_dict(py);
-            let pyerr = py.run("raise err", None, Some(locals)).unwrap_err();
+            let locals = [("err", pyerr)].into_py_dict(py).as_borrowed();
+            let pyerr = py.run_bound("raise err", None, Some(&locals)).unwrap_err();
             assert_eq!(pyerr.value(py).to_string(), expected_contents);
         })
     }
@@ -164,8 +164,8 @@ mod test_anyhow {
         let pyerr = PyErr::from(err);
 
         Python::with_gil(|py| {
-            let locals = [("err", pyerr)].into_py_dict(py);
-            let pyerr = py.run("raise err", None, Some(locals)).unwrap_err();
+            let locals = [("err", pyerr)].into_py_dict(py).as_borrowed();
+            let pyerr = py.run_bound("raise err", None, Some(&locals)).unwrap_err();
             assert_eq!(pyerr.value(py).to_string(), expected_contents);
         })
     }
diff --git a/src/conversions/chrono.rs b/src/conversions/chrono.rs
index 83f9830b..069a137f 100644
--- a/src/conversions/chrono.rs
+++ b/src/conversions/chrono.rs
@@ -574,12 +574,15 @@ mod tests {
     // tzdata there to make this work.
     #[cfg(all(Py_3_9, not(target_os = "windows")))]
     fn test_zoneinfo_is_not_fixed_offset() {
+        use crate::types::any::PyAnyMethods;
+        use crate::types::dict::PyDictMethods;
+
         Python::with_gil(|py| {
-            let locals = crate::types::PyDict::new(py);
-            py.run(
+            let locals = crate::types::PyDict::new_bound(py);
+            py.run_bound(
                 "import zoneinfo; zi = zoneinfo.ZoneInfo('Europe/London')",
                 None,
-                Some(locals),
+                Some(&locals),
             )
             .unwrap();
             let result: PyResult<FixedOffset> = locals.get_item("zi").unwrap().unwrap().extract();
diff --git a/src/conversions/eyre.rs b/src/conversions/eyre.rs
index b0559ad1..7f029cf6 100644
--- a/src/conversions/eyre.rs
+++ b/src/conversions/eyre.rs
@@ -152,8 +152,8 @@ mod tests {
         let pyerr = PyErr::from(err);
 
         Python::with_gil(|py| {
-            let locals = [("err", pyerr)].into_py_dict(py);
-            let pyerr = py.run("raise err", None, Some(locals)).unwrap_err();
+            let locals = [("err", pyerr)].into_py_dict(py).as_borrowed();
+            let pyerr = py.run_bound("raise err", None, Some(&locals)).unwrap_err();
             assert_eq!(pyerr.value(py).to_string(), expected_contents);
         })
     }
@@ -169,8 +169,8 @@ mod tests {
         let pyerr = PyErr::from(err);
 
         Python::with_gil(|py| {
-            let locals = [("err", pyerr)].into_py_dict(py);
-            let pyerr = py.run("raise err", None, Some(locals)).unwrap_err();
+            let locals = [("err", pyerr)].into_py_dict(py).as_borrowed();
+            let pyerr = py.run_bound("raise err", None, Some(&locals)).unwrap_err();
             assert_eq!(pyerr.value(py).to_string(), expected_contents);
         })
     }
diff --git a/src/conversions/rust_decimal.rs b/src/conversions/rust_decimal.rs
index 2e38e780..e829e883 100644
--- a/src/conversions/rust_decimal.rs
+++ b/src/conversions/rust_decimal.rs
@@ -108,6 +108,8 @@ impl IntoPy<PyObject> for Decimal {
 mod test_rust_decimal {
     use super::*;
     use crate::err::PyErr;
+    use crate::types::any::PyAnyMethods;
+    use crate::types::dict::PyDictMethods;
     use crate::types::PyDict;
     use rust_decimal::Decimal;
 
@@ -121,16 +123,16 @@ mod test_rust_decimal {
                 Python::with_gil(|py| {
                     let rs_orig = $rs;
                     let rs_dec = rs_orig.into_py(py);
-                    let locals = PyDict::new(py);
+                    let locals = PyDict::new_bound(py);
                     locals.set_item("rs_dec", &rs_dec).unwrap();
                     // Checks if Rust Decimal -> Python Decimal conversion is correct
-                    py.run(
+                    py.run_bound(
                         &format!(
                             "import decimal\npy_dec = decimal.Decimal({})\nassert py_dec == rs_dec",
                             $py
                         ),
                         None,
-                        Some(locals),
+                        Some(&locals),
                     )
                     .unwrap();
                     // Checks if Python Decimal -> Rust Decimal conversion is correct
@@ -163,13 +165,13 @@ mod test_rust_decimal {
             let num = Decimal::from_parts(lo, mid, high, negative, scale);
             Python::with_gil(|py| {
                 let rs_dec = num.into_py(py);
-                let locals = PyDict::new(py);
+                let locals = PyDict::new_bound(py);
                 locals.set_item("rs_dec", &rs_dec).unwrap();
-                py.run(
+                py.run_bound(
                     &format!(
                        "import decimal\npy_dec = decimal.Decimal(\"{}\")\nassert py_dec == rs_dec",
                      num),
-                None, Some(locals)).unwrap();
+                None, Some(&locals)).unwrap();
                 let roundtripped: Decimal = rs_dec.extract(py).unwrap();
                 assert_eq!(num, roundtripped);
             })
@@ -189,11 +191,11 @@ mod test_rust_decimal {
     #[test]
     fn test_nan() {
         Python::with_gil(|py| {
-            let locals = PyDict::new(py);
-            py.run(
+            let locals = PyDict::new_bound(py);
+            py.run_bound(
                 "import decimal\npy_dec = decimal.Decimal(\"NaN\")",
                 None,
-                Some(locals),
+                Some(&locals),
             )
             .unwrap();
             let py_dec = locals.get_item("py_dec").unwrap().unwrap();
@@ -205,11 +207,11 @@ mod test_rust_decimal {
     #[test]
     fn test_infinity() {
         Python::with_gil(|py| {
-            let locals = PyDict::new(py);
-            py.run(
+            let locals = PyDict::new_bound(py);
+            py.run_bound(
                 "import decimal\npy_dec = decimal.Decimal(\"Infinity\")",
                 None,
-                Some(locals),
+                Some(&locals),
             )
             .unwrap();
             let py_dec = locals.get_item("py_dec").unwrap().unwrap();
diff --git a/src/conversions/std/num.rs b/src/conversions/std/num.rs
index 2d20915d..75c2e16b 100644
--- a/src/conversions/std/num.rs
+++ b/src/conversions/std/num.rs
@@ -376,6 +376,9 @@ mod test_128bit_integers {
     #[cfg(not(target_arch = "wasm32"))]
     use crate::types::PyDict;
 
+    #[cfg(not(target_arch = "wasm32"))]
+    use crate::types::dict::PyDictMethods;
+
     #[cfg(not(target_arch = "wasm32"))]
     use proptest::prelude::*;
 
@@ -385,9 +388,9 @@ mod test_128bit_integers {
         fn test_i128_roundtrip(x: i128) {
             Python::with_gil(|py| {
                 let x_py = x.into_py(py);
-                let locals = PyDict::new(py);
+                let locals = PyDict::new_bound(py);
                 locals.set_item("x_py", x_py.clone_ref(py)).unwrap();
-                py.run(&format!("assert x_py == {}", x), None, Some(locals)).unwrap();
+                py.run_bound(&format!("assert x_py == {}", x), None, Some(&locals)).unwrap();
                 let roundtripped: i128 = x_py.extract(py).unwrap();
                 assert_eq!(x, roundtripped);
             })
@@ -401,9 +404,9 @@ mod test_128bit_integers {
         ) {
             Python::with_gil(|py| {
                 let x_py = x.into_py(py);
-                let locals = PyDict::new(py);
+                let locals = PyDict::new_bound(py);
                 locals.set_item("x_py", x_py.clone_ref(py)).unwrap();
-                py.run(&format!("assert x_py == {}", x), None, Some(locals)).unwrap();
+                py.run_bound(&format!("assert x_py == {}", x), None, Some(&locals)).unwrap();
                 let roundtripped: NonZeroI128 = x_py.extract(py).unwrap();
                 assert_eq!(x, roundtripped);
             })
@@ -416,9 +419,9 @@ mod test_128bit_integers {
         fn test_u128_roundtrip(x: u128) {
             Python::with_gil(|py| {
                 let x_py = x.into_py(py);
-                let locals = PyDict::new(py);
+                let locals = PyDict::new_bound(py);
                 locals.set_item("x_py", x_py.clone_ref(py)).unwrap();
-                py.run(&format!("assert x_py == {}", x), None, Some(locals)).unwrap();
+                py.run_bound(&format!("assert x_py == {}", x), None, Some(&locals)).unwrap();
                 let roundtripped: u128 = x_py.extract(py).unwrap();
                 assert_eq!(x, roundtripped);
             })
@@ -432,9 +435,9 @@ mod test_128bit_integers {
         ) {
             Python::with_gil(|py| {
                 let x_py = x.into_py(py);
-                let locals = PyDict::new(py);
+                let locals = PyDict::new_bound(py);
                 locals.set_item("x_py", x_py.clone_ref(py)).unwrap();
-                py.run(&format!("assert x_py == {}", x), None, Some(locals)).unwrap();
+                py.run_bound(&format!("assert x_py == {}", x), None, Some(&locals)).unwrap();
                 let roundtripped: NonZeroU128 = x_py.extract(py).unwrap();
                 assert_eq!(x, roundtripped);
             })
diff --git a/src/err/mod.rs b/src/err/mod.rs
index 85685456..e53a9657 100644
--- a/src/err/mod.rs
+++ b/src/err/mod.rs
@@ -1030,7 +1030,7 @@ mod tests {
 
         Python::with_gil(|py| {
             let err = py
-                .run("raise Exception('banana')", None, None)
+                .run_bound("raise Exception('banana')", None, None)
                 .expect_err("raising should have given us an error");
 
             let debug_str = format!("{:?}", err);
@@ -1055,7 +1055,7 @@ mod tests {
     fn err_display() {
         Python::with_gil(|py| {
             let err = py
-                .run("raise Exception('banana')", None, None)
+                .run_bound("raise Exception('banana')", None, None)
                 .expect_err("raising should have given us an error");
             assert_eq!(err.to_string(), "Exception: banana");
         });
@@ -1102,12 +1102,12 @@ mod tests {
     fn test_pyerr_cause() {
         Python::with_gil(|py| {
             let err = py
-                .run("raise Exception('banana')", None, None)
+                .run_bound("raise Exception('banana')", None, None)
                 .expect_err("raising should have given us an error");
             assert!(err.cause(py).is_none());
 
             let err = py
-                .run(
+                .run_bound(
                     "raise Exception('banana') from Exception('apple')",
                     None,
                     None,
diff --git a/src/exceptions.rs b/src/exceptions.rs
index daea55e5..10121b8a 100644
--- a/src/exceptions.rs
+++ b/src/exceptions.rs
@@ -165,18 +165,18 @@ macro_rules! import_exception {
 /// # fn main() -> PyResult<()> {
 /// #     Python::with_gil(|py| -> PyResult<()> {
 /// #         let fun = wrap_pyfunction!(raise_myerror, py)?;
-/// #         let locals = pyo3::types::PyDict::new(py);
+/// #         let locals = pyo3::types::PyDict::new_bound(py);
 /// #         locals.set_item("MyError", py.get_type::<MyError>())?;
 /// #         locals.set_item("raise_myerror", fun)?;
 /// #
-/// #         py.run(
+/// #         py.run_bound(
 /// # "try:
 /// #     raise_myerror()
 /// # except MyError as e:
 /// #     assert e.__doc__ == 'Some description.'
 /// #     assert str(e) == 'Some error happened.'",
 /// #             None,
-/// #             Some(locals),
+/// #             Some(&locals),
 /// #         )?;
 /// #
 /// #         Ok(())
@@ -338,7 +338,7 @@ use pyo3::prelude::*;
 use pyo3::exceptions::Py", $name, ";
 
 Python::with_gil(|py| {
-    let result: PyResult<()> = py.run(\"raise ", $name, "\", None, None);
+    let result: PyResult<()> = py.run_bound(\"raise ", $name, "\", None, None);
 
     let error_type = match result {
         Ok(_) => \"Not an error\",
@@ -816,7 +816,7 @@ mod tests {
                 .map_err(|e| e.display(py))
                 .expect("could not import socket");
 
-            let d = PyDict::new(py);
+            let d = PyDict::new_bound(py);
             d.set_item("socket", socket)
                 .map_err(|e| e.display(py))
                 .expect("could not setitem");
@@ -825,7 +825,7 @@ mod tests {
                 .map_err(|e| e.display(py))
                 .expect("could not setitem");
 
-            py.run("assert isinstance(exc, socket.gaierror)", None, Some(d))
+            py.run_bound("assert isinstance(exc, socket.gaierror)", None, Some(&d))
                 .map_err(|e| e.display(py))
                 .expect("assertion failed");
         });
@@ -840,7 +840,7 @@ mod tests {
                 .map_err(|e| e.display(py))
                 .expect("could not import email");
 
-            let d = PyDict::new(py);
+            let d = PyDict::new_bound(py);
             d.set_item("email", email)
                 .map_err(|e| e.display(py))
                 .expect("could not setitem");
@@ -848,10 +848,10 @@ mod tests {
                 .map_err(|e| e.display(py))
                 .expect("could not setitem");
 
-            py.run(
+            py.run_bound(
                 "assert isinstance(exc, email.errors.MessageError)",
                 None,
-                Some(d),
+                Some(&d),
             )
             .map_err(|e| e.display(py))
             .expect("assertion failed");
@@ -871,14 +871,13 @@ mod tests {
                 .extract()
                 .unwrap();
             assert_eq!(type_description, "<class 'mymodule.CustomError'>");
-            let ctx = ctx.as_gil_ref();
-            py.run(
+            py.run_bound(
                 "assert CustomError('oops').args == ('oops',)",
                 None,
-                Some(ctx),
+                Some(&ctx),
             )
             .unwrap();
-            py.run("assert CustomError.__doc__ is None", None, Some(ctx))
+            py.run_bound("assert CustomError.__doc__ is None", None, Some(&ctx))
                 .unwrap();
         });
     }
@@ -914,15 +913,18 @@ mod tests {
                 .extract()
                 .unwrap();
             assert_eq!(type_description, "<class 'mymodule.CustomError'>");
-            let ctx = ctx.as_gil_ref();
-            py.run(
+            py.run_bound(
                 "assert CustomError('oops').args == ('oops',)",
                 None,
-                Some(ctx),
+                Some(&ctx),
+            )
+            .unwrap();
+            py.run_bound(
+                "assert CustomError.__doc__ == 'Some docs'",
+                None,
+                Some(&ctx),
             )
             .unwrap();
-            py.run("assert CustomError.__doc__ == 'Some docs'", None, Some(ctx))
-                .unwrap();
         });
     }
 
@@ -944,17 +946,16 @@ mod tests {
                 .extract()
                 .unwrap();
             assert_eq!(type_description, "<class 'mymodule.CustomError'>");
-            let ctx = ctx.as_gil_ref();
-            py.run(
+            py.run_bound(
                 "assert CustomError('oops').args == ('oops',)",
                 None,
-                Some(ctx),
+                Some(&ctx),
             )
             .unwrap();
-            py.run(
+            py.run_bound(
                 "assert CustomError.__doc__ == 'Some more docs'",
                 None,
-                Some(ctx),
+                Some(&ctx),
             )
             .unwrap();
         });
@@ -964,7 +965,7 @@ mod tests {
     fn native_exception_debug() {
         Python::with_gil(|py| {
             let exc = py
-                .run("raise Exception('banana')", None, None)
+                .run_bound("raise Exception('banana')", None, None)
                 .expect_err("raising should have given us an error")
                 .into_value(py)
                 .into_ref(py);
@@ -979,7 +980,7 @@ mod tests {
     fn native_exception_display() {
         Python::with_gil(|py| {
             let exc = py
-                .run("raise Exception('banana')", None, None)
+                .run_bound("raise Exception('banana')", None, None)
                 .expect_err("raising should have given us an error")
                 .into_value(py)
                 .into_ref(py);
@@ -996,7 +997,7 @@ mod tests {
 
         Python::with_gil(|py| {
             let exc = py
-                .run(
+                .run_bound(
                     "raise Exception('banana') from TypeError('peach')",
                     None,
                     None,
diff --git a/src/ffi/tests.rs b/src/ffi/tests.rs
index fc10bf05..0735e456 100644
--- a/src/ffi/tests.rs
+++ b/src/ffi/tests.rs
@@ -20,12 +20,12 @@ fn test_datetime_fromtimestamp() {
             PyDateTime_IMPORT();
             py.from_owned_ptr(PyDateTime_FromTimestamp(args.as_ptr()))
         };
-        let locals = PyDict::new(py);
+        let locals = PyDict::new_bound(py);
         locals.set_item("dt", dt).unwrap();
-        py.run(
+        py.run_bound(
             "import datetime; assert dt == datetime.datetime.fromtimestamp(100)",
             None,
-            Some(locals),
+            Some(&locals),
         )
         .unwrap();
     })
@@ -41,12 +41,12 @@ fn test_date_fromtimestamp() {
             PyDateTime_IMPORT();
             py.from_owned_ptr(PyDate_FromTimestamp(args.as_ptr()))
         };
-        let locals = PyDict::new(py);
+        let locals = PyDict::new_bound(py);
         locals.set_item("dt", dt).unwrap();
-        py.run(
+        py.run_bound(
             "import datetime; assert dt == datetime.date.fromtimestamp(100)",
             None,
-            Some(locals),
+            Some(&locals),
         )
         .unwrap();
     })
@@ -61,12 +61,12 @@ fn test_utc_timezone() {
             PyDateTime_IMPORT();
             py.from_borrowed_ptr(PyDateTime_TimeZone_UTC())
         };
-        let locals = PyDict::new(py);
+        let locals = PyDict::new_bound(py);
         locals.set_item("utc_timezone", utc_timezone).unwrap();
-        py.run(
+        py.run_bound(
             "import datetime; assert utc_timezone is datetime.timezone.utc",
             None,
-            Some(locals),
+            Some(&locals),
         )
         .unwrap();
     })
diff --git a/src/gil.rs b/src/gil.rs
index 61d69ed9..379dab4b 100644
--- a/src/gil.rs
+++ b/src/gil.rs
@@ -75,7 +75,7 @@ fn gil_is_acquired() -> bool {
 ///
 /// # fn main() -> PyResult<()> {
 /// pyo3::prepare_freethreaded_python();
-/// Python::with_gil(|py| py.run("print('Hello World')", None, None))
+/// Python::with_gil(|py| py.run_bound("print('Hello World')", None, None))
 /// # }
 /// ```
 #[cfg(not(PyPy))]
@@ -118,7 +118,7 @@ pub fn prepare_freethreaded_python() {
 /// ```rust
 /// unsafe {
 ///     pyo3::with_embedded_python_interpreter(|py| {
-///         if let Err(e) = py.run("print('Hello World')", None, None) {
+///         if let Err(e) = py.run_bound("print('Hello World')", None, None) {
 ///             // We must make sure to not return a `PyErr`!
 ///             e.print(py);
 ///         }
diff --git a/src/macros.rs b/src/macros.rs
index 41de9079..79e8ea58 100644
--- a/src/macros.rs
+++ b/src/macros.rs
@@ -104,12 +104,13 @@ macro_rules! py_run_impl {
     }};
     ($py:expr, *$dict:expr, $code:expr) => {{
         use ::std::option::Option::*;
-        if let ::std::result::Result::Err(e) = $py.run($code, None, Some($dict)) {
+        use $crate::PyNativeType;
+        if let ::std::result::Result::Err(e) = $py.run_bound($code, None, Some(&$dict.as_borrowed())) {
             e.print($py);
             // So when this c api function the last line called printed the error to stderr,
             // the output is only written into a buffer which is never flushed because we
             // panic before flushing. This is where this hack comes into place
-            $py.run("import sys; sys.stderr.flush()", None, None)
+            $py.run_bound("import sys; sys.stderr.flush()", None, None)
                 .unwrap();
             ::std::panic!("{}", $code)
         }
diff --git a/src/marker.rs b/src/marker.rs
index 1802d858..121cfe68 100644
--- a/src/marker.rs
+++ b/src/marker.rs
@@ -600,6 +600,27 @@ impl<'py> Python<'py> {
         self.run_code(code, ffi::Py_eval_input, globals, locals)
     }
 
+    /// Deprecated version of [`Python::run_bound`]
+    #[cfg_attr(
+        not(feature = "gil-refs"),
+        deprecated(
+            since = "0.21.0",
+            note = "`Python::run` will be replaced by `Python::run_bound` in a future PyO3 version"
+        )
+    )]
+    pub fn run(
+        self,
+        code: &str,
+        globals: Option<&PyDict>,
+        locals: Option<&PyDict>,
+    ) -> PyResult<()> {
+        self.run_bound(
+            code,
+            globals.map(PyNativeType::as_borrowed).as_deref(),
+            locals.map(PyNativeType::as_borrowed).as_deref(),
+        )
+    }
+
     /// Executes one or more Python statements in the given context.
     ///
     /// If `globals` is `None`, it defaults to Python module `__main__`.
@@ -615,37 +636,32 @@ impl<'py> Python<'py> {
     ///     types::{PyBytes, PyDict},
     /// };
     /// Python::with_gil(|py| {
-    ///     let locals = PyDict::new(py);
-    ///     py.run(
+    ///     let locals = PyDict::new_bound(py);
+    ///     py.run_bound(
     ///         r#"
     /// import base64
     /// s = 'Hello Rust!'
     /// ret = base64.b64encode(s.encode('utf-8'))
     /// "#,
     ///         None,
-    ///         Some(locals),
+    ///         Some(&locals),
     ///     )
     ///     .unwrap();
     ///     let ret = locals.get_item("ret").unwrap().unwrap();
-    ///     let b64: &PyBytes = ret.downcast().unwrap();
+    ///     let b64 = ret.downcast::<PyBytes>().unwrap();
     ///     assert_eq!(b64.as_bytes(), b"SGVsbG8gUnVzdCE=");
     /// });
     /// ```
     ///
     /// You can use [`py_run!`](macro.py_run.html) for a handy alternative of `run`
     /// if you don't need `globals` and unwrapping is OK.
-    pub fn run(
+    pub fn run_bound(
         self,
         code: &str,
-        globals: Option<&PyDict>,
-        locals: Option<&PyDict>,
+        globals: Option<&Bound<'py, PyDict>>,
+        locals: Option<&Bound<'py, PyDict>>,
     ) -> PyResult<()> {
-        let res = self.run_code(
-            code,
-            ffi::Py_file_input,
-            globals.map(PyNativeType::as_borrowed).as_deref(),
-            locals.map(PyNativeType::as_borrowed).as_deref(),
-        );
+        let res = self.run_code(code, ffi::Py_file_input, globals, locals);
         res.map(|obj| {
             debug_assert!(obj.is_none());
         })
@@ -1235,9 +1251,11 @@ mod tests {
 
     #[test]
     fn test_py_run_inserts_globals() {
+        use crate::types::dict::PyDictMethods;
+
         Python::with_gil(|py| {
-            let namespace = PyDict::new(py);
-            py.run("class Foo: pass", Some(namespace), Some(namespace))
+            let namespace = PyDict::new_bound(py);
+            py.run_bound("class Foo: pass", Some(&namespace), Some(&namespace))
                 .unwrap();
             assert!(matches!(namespace.get_item("Foo"), Ok(Some(..))));
             assert!(matches!(namespace.get_item("__builtins__"), Ok(Some(..))));
diff --git a/src/tests/common.rs b/src/tests/common.rs
index efab3ccb..e424c1ca 100644
--- a/src/tests/common.rs
+++ b/src/tests/common.rs
@@ -40,7 +40,8 @@ mod inner {
         }};
         // Case2: dict & no err_msg
         ($py:expr, *$dict:expr, $code:expr, $err:ident) => {{
-            let res = $py.run($code, None, Some($dict));
+            use pyo3::PyNativeType;
+            let res = $py.run_bound($code, None, Some(&$dict.as_borrowed()));
             let err = res.expect_err(&format!("Did not raise {}", stringify!($err)));
             if !err.matches($py, $py.get_type::<pyo3::exceptions::$err>()) {
                 panic!("Expected {} but got {:?}", stringify!($err), err)
diff --git a/src/types/bytearray.rs b/src/types/bytearray.rs
index 6303a87d..7f0fdf9e 100644
--- a/src/types/bytearray.rs
+++ b/src/types/bytearray.rs
@@ -197,10 +197,10 @@ impl PyByteArray {
     /// # fn main() -> PyResult<()> {
     /// #     Python::with_gil(|py| -> PyResult<()> {
     /// #         let fun = wrap_pyfunction!(a_valid_function, py)?;
-    /// #         let locals = pyo3::types::PyDict::new(py);
+    /// #         let locals = pyo3::types::PyDict::new_bound(py);
     /// #         locals.set_item("a_valid_function", fun)?;
     /// #
-    /// #         py.run(
+    /// #         py.run_bound(
     /// # r#"b = bytearray(b"hello world")
     /// # a_valid_function(b)
     /// #
@@ -209,7 +209,7 @@ impl PyByteArray {
     /// # except RuntimeError as e:
     /// #     assert str(e) == 'input is not long enough'"#,
     /// #             None,
-    /// #             Some(locals),
+    /// #             Some(&locals),
     /// #         )?;
     /// #
     /// #         Ok(())
@@ -359,10 +359,10 @@ pub trait PyByteArrayMethods<'py> {
     /// # fn main() -> PyResult<()> {
     /// #     Python::with_gil(|py| -> PyResult<()> {
     /// #         let fun = wrap_pyfunction!(a_valid_function, py)?;
-    /// #         let locals = pyo3::types::PyDict::new(py);
+    /// #         let locals = pyo3::types::PyDict::new_bound(py);
     /// #         locals.set_item("a_valid_function", fun)?;
     /// #
-    /// #         py.run(
+    /// #         py.run_bound(
     /// # r#"b = bytearray(b"hello world")
     /// # a_valid_function(b)
     /// #
@@ -371,7 +371,7 @@ pub trait PyByteArrayMethods<'py> {
     /// # except RuntimeError as e:
     /// #     assert str(e) == 'input is not long enough'"#,
     /// #             None,
-    /// #             Some(locals),
+    /// #             Some(&locals),
     /// #         )?;
     /// #
     /// #         Ok(())
diff --git a/src/types/traceback.rs b/src/types/traceback.rs
index 84ecda74..3608772f 100644
--- a/src/types/traceback.rs
+++ b/src/types/traceback.rs
@@ -28,7 +28,7 @@ impl PyTraceback {
     /// # let result: PyResult<()> =
     /// Python::with_gil(|py| {
     ///     let err = py
-    ///         .run("raise Exception('banana')", None, None)
+    ///         .run_bound("raise Exception('banana')", None, None)
     ///         .expect_err("raise will create a Python error");
     ///
     ///     let traceback = err.traceback_bound(py).expect("raised exception will have a traceback");
@@ -71,7 +71,7 @@ pub trait PyTracebackMethods<'py> {
     /// # let result: PyResult<()> =
     /// Python::with_gil(|py| {
     ///     let err = py
-    ///         .run("raise Exception('banana')", None, None)
+    ///         .run_bound("raise Exception('banana')", None, None)
     ///         .expect_err("raise will create a Python error");
     ///
     ///     let traceback = err.traceback_bound(py).expect("raised exception will have a traceback");
@@ -121,7 +121,7 @@ mod tests {
     fn format_traceback() {
         Python::with_gil(|py| {
             let err = py
-                .run("raise Exception('banana')", None, None)
+                .run_bound("raise Exception('banana')", None, None)
                 .expect_err("raising should have given us an error");
 
             assert_eq!(
@@ -134,9 +134,9 @@ mod tests {
     #[test]
     fn test_err_from_value() {
         Python::with_gil(|py| {
-            let locals = PyDict::new(py);
+            let locals = PyDict::new_bound(py);
             // Produce an error from python so that it has a traceback
-            py.run(
+            py.run_bound(
                 r"
 try:
     raise ValueError('raised exception')
@@ -144,10 +144,10 @@ except Exception as e:
     err = e
 ",
                 None,
-                Some(locals),
+                Some(&locals),
             )
             .unwrap();
-            let err = PyErr::from_value(locals.get_item("err").unwrap().unwrap());
+            let err = PyErr::from_value(locals.get_item("err").unwrap().unwrap().into_gil_ref());
             let traceback = err.value(py).getattr("__traceback__").unwrap();
             assert!(err.traceback_bound(py).unwrap().is(traceback));
         })
@@ -156,15 +156,15 @@ except Exception as e:
     #[test]
     fn test_err_into_py() {
         Python::with_gil(|py| {
-            let locals = PyDict::new(py);
+            let locals = PyDict::new_bound(py);
             // Produce an error from python so that it has a traceback
-            py.run(
+            py.run_bound(
                 r"
 def f():
     raise ValueError('raised exception')
 ",
                 None,
-                Some(locals),
+                Some(&locals),
             )
             .unwrap();
             let f = locals.get_item("f").unwrap().unwrap();
diff --git a/tests/test_anyhow.rs b/tests/test_anyhow.rs
index f0df4dcc..1807cfe9 100644
--- a/tests/test_anyhow.rs
+++ b/tests/test_anyhow.rs
@@ -25,6 +25,7 @@ fn test_anyhow_py_function_ok_result() {
 
 #[test]
 fn test_anyhow_py_function_err_result() {
+    use pyo3::prelude::PyDictMethods;
     use pyo3::{pyfunction, types::PyDict, wrap_pyfunction, Python};
 
     #[pyfunction]
@@ -34,15 +35,15 @@ fn test_anyhow_py_function_err_result() {
 
     Python::with_gil(|py| {
         let func = wrap_pyfunction!(produce_err_result)(py).unwrap();
-        let locals = PyDict::new(py);
+        let locals = PyDict::new_bound(py);
         locals.set_item("func", func).unwrap();
 
-        py.run(
+        py.run_bound(
             r#"
             func()
             "#,
             None,
-            Some(locals),
+            Some(&locals),
         )
         .unwrap_err();
     });
diff --git a/tests/test_append_to_inittab.rs b/tests/test_append_to_inittab.rs
index e0a57da1..00cccdbb 100644
--- a/tests/test_append_to_inittab.rs
+++ b/tests/test_append_to_inittab.rs
@@ -18,7 +18,7 @@ fn test_module_append_to_inittab() {
     use pyo3::append_to_inittab;
     append_to_inittab!(module_with_functions);
     Python::with_gil(|py| {
-        py.run(
+        py.run_bound(
             r#"
 import module_with_functions
 assert module_with_functions.foo() == 123
diff --git a/tests/test_class_new.rs b/tests/test_class_new.rs
index 8cb42686..8084be05 100644
--- a/tests/test_class_new.rs
+++ b/tests/test_class_new.rs
@@ -169,9 +169,12 @@ c = Class()
 assert c.from_rust is False
 "#
         );
-        let globals = PyModule::import(py, "__main__").unwrap().dict();
+        let globals = PyModule::import(py, "__main__")
+            .unwrap()
+            .dict()
+            .as_borrowed();
         globals.set_item("SuperClass", super_cls).unwrap();
-        py.run(source, Some(globals), None)
+        py.run_bound(source, Some(&globals), None)
             .map_err(|e| e.display(py))
             .unwrap();
     });
diff --git a/tests/test_coroutine.rs b/tests/test_coroutine.rs
index 206c35da..d9672cd6 100644
--- a/tests/test_coroutine.rs
+++ b/tests/test_coroutine.rs
@@ -127,12 +127,12 @@ fn cancelled_coroutine() {
             await task
         asyncio.run(main())
         "#;
-        let globals = gil.import("__main__").unwrap().dict();
+        let globals = gil.import("__main__").unwrap().dict().as_borrowed();
         globals.set_item("sleep", sleep).unwrap();
         let err = gil
-            .run(
+            .run_bound(
                 &pyo3::unindent::unindent(&handle_windows(test)),
-                Some(globals),
+                Some(&globals),
                 None,
             )
             .unwrap_err();
@@ -166,13 +166,13 @@ fn coroutine_cancel_handle() {
             return await task
         assert asyncio.run(main()) == 0
         "#;
-        let globals = gil.import("__main__").unwrap().dict();
+        let globals = gil.import("__main__").unwrap().dict().as_borrowed();
         globals
             .set_item("cancellable_sleep", cancellable_sleep)
             .unwrap();
-        gil.run(
+        gil.run_bound(
             &pyo3::unindent::unindent(&handle_windows(test)),
-            Some(globals),
+            Some(&globals),
             None,
         )
         .unwrap();
@@ -198,11 +198,11 @@ fn coroutine_is_cancelled() {
             await task
         asyncio.run(main())
         "#;
-        let globals = gil.import("__main__").unwrap().dict();
+        let globals = gil.import("__main__").unwrap().dict().as_borrowed();
         globals.set_item("sleep_loop", sleep_loop).unwrap();
-        gil.run(
+        gil.run_bound(
             &pyo3::unindent::unindent(&handle_windows(test)),
-            Some(globals),
+            Some(&globals),
             None,
         )
         .unwrap();
diff --git a/tests/test_datetime.rs b/tests/test_datetime.rs
index bfde37d3..d1efd1ef 100644
--- a/tests/test_datetime.rs
+++ b/tests/test_datetime.rs
@@ -12,14 +12,16 @@ fn _get_subclasses<'py>(
     // Import the class from Python and create some subclasses
     let datetime = py.import("datetime")?;
 
-    let locals = [(py_type, datetime.getattr(py_type)?)].into_py_dict(py);
+    let locals = [(py_type, datetime.getattr(py_type)?)]
+        .into_py_dict(py)
+        .as_borrowed();
 
     let make_subclass_py = format!("class Subklass({}):\n    pass", py_type);
 
     let make_sub_subclass_py = "class SubSubklass(Subklass):\n    pass";
 
-    py.run(&make_subclass_py, None, Some(locals))?;
-    py.run(make_sub_subclass_py, None, Some(locals))?;
+    py.run_bound(&make_subclass_py, None, Some(&locals))?;
+    py.run_bound(make_sub_subclass_py, None, Some(&locals))?;
 
     let locals = locals.as_borrowed();
     // Construct an instance of the base class
diff --git a/tests/test_gc.rs b/tests/test_gc.rs
index 43cdb1b4..7ed39436 100644
--- a/tests/test_gc.rs
+++ b/tests/test_gc.rs
@@ -117,7 +117,7 @@ fn gc_integration() {
     });
 
     Python::with_gil(|py| {
-        py.run("import gc; gc.collect()", None, None).unwrap();
+        py.run_bound("import gc; gc.collect()", None, None).unwrap();
         assert!(drop_called.load(Ordering::Relaxed));
     });
 }
@@ -156,7 +156,7 @@ fn gc_null_traversal() {
         obj.borrow_mut(py).cycle = Some(obj.clone_ref(py));
 
         // the object doesn't have to be cleaned up, it just needs to be traversed.
-        py.run("import gc; gc.collect()", None, None).unwrap();
+        py.run_bound("import gc; gc.collect()", None, None).unwrap();
     });
 }
 
@@ -469,7 +469,7 @@ fn drop_during_traversal_with_gil() {
     // (but not too many) collections to get `inst` actually dropped.
     for _ in 0..10 {
         Python::with_gil(|py| {
-            py.run("import gc; gc.collect()", None, None).unwrap();
+            py.run_bound("import gc; gc.collect()", None, None).unwrap();
         });
     }
     assert!(drop_called.load(Ordering::Relaxed));
@@ -502,7 +502,7 @@ fn drop_during_traversal_without_gil() {
     // (but not too many) collections to get `inst` actually dropped.
     for _ in 0..10 {
         Python::with_gil(|py| {
-            py.run("import gc; gc.collect()", None, None).unwrap();
+            py.run_bound("import gc; gc.collect()", None, None).unwrap();
         });
     }
     assert!(drop_called.load(Ordering::Relaxed));
diff --git a/tests/test_inheritance.rs b/tests/test_inheritance.rs
index 16f87df9..4b024ed7 100644
--- a/tests/test_inheritance.rs
+++ b/tests/test_inheritance.rs
@@ -20,12 +20,14 @@ struct SubclassAble {}
 #[test]
 fn subclass() {
     Python::with_gil(|py| {
-        let d = [("SubclassAble", py.get_type::<SubclassAble>())].into_py_dict(py);
+        let d = [("SubclassAble", py.get_type::<SubclassAble>())]
+            .into_py_dict(py)
+            .as_borrowed();
 
-        py.run(
+        py.run_bound(
             "class A(SubclassAble): pass\nassert issubclass(A, SubclassAble)",
             None,
-            Some(d),
+            Some(&d),
         )
         .map_err(|e| e.display(py))
         .unwrap();
@@ -97,9 +99,13 @@ fn call_base_and_sub_methods() {
 fn mutation_fails() {
     Python::with_gil(|py| {
         let obj = PyCell::new(py, SubClass::new()).unwrap();
-        let global = Some([("obj", obj)].into_py_dict(py));
+        let global = [("obj", obj)].into_py_dict(py).as_borrowed();
         let e = py
-            .run("obj.base_set(lambda: obj.sub_set_and_ret(1))", global, None)
+            .run_bound(
+                "obj.base_set(lambda: obj.sub_set_and_ret(1))",
+                Some(&global),
+                None,
+            )
             .unwrap_err();
         assert_eq!(&e.to_string(), "RuntimeError: Already borrowed");
     });
@@ -271,11 +277,11 @@ mod inheriting_native_type {
     fn custom_exception() {
         Python::with_gil(|py| {
             let cls = py.get_type::<CustomException>();
-            let dict = [("cls", cls)].into_py_dict(py);
-            let res = py.run(
+            let dict = [("cls", cls)].into_py_dict(py).as_borrowed();
+            let res = py.run_bound(
             "e = cls('hello'); assert str(e) == 'hello'; assert e.context == 'Hello :)'; raise e",
             None,
-            Some(dict)
+            Some(&dict)
             );
             let err = res.unwrap_err();
             assert!(err.matches(py, cls), "{}", err);
diff --git a/tests/test_proto_methods.rs b/tests/test_proto_methods.rs
index 50dd99ce..b1fe7548 100644
--- a/tests/test_proto_methods.rs
+++ b/tests/test_proto_methods.rs
@@ -687,9 +687,12 @@ if sys.platform == "win32" and sys.version_info >= (3, 8, 0):
 
 asyncio.run(main())
 "#;
-        let globals = PyModule::import(py, "__main__").unwrap().dict();
+        let globals = PyModule::import(py, "__main__")
+            .unwrap()
+            .dict()
+            .as_borrowed();
         globals.set_item("Once", once).unwrap();
-        py.run(source, Some(globals), None)
+        py.run_bound(source, Some(&globals), None)
             .map_err(|e| e.display(py))
             .unwrap();
     });
@@ -741,12 +744,15 @@ if sys.platform == "win32" and sys.version_info >= (3, 8, 0):
 
 asyncio.run(main())
 "#;
-        let globals = PyModule::import(py, "__main__").unwrap().dict();
+        let globals = PyModule::import(py, "__main__")
+            .unwrap()
+            .dict()
+            .as_borrowed();
         globals.set_item("Once", once).unwrap();
         globals
             .set_item("AsyncIterator", py.get_type::<AsyncIterator>())
             .unwrap();
-        py.run(source, Some(globals), None)
+        py.run_bound(source, Some(&globals), None)
             .map_err(|e| e.display(py))
             .unwrap();
     });
@@ -813,9 +819,12 @@ del c.counter
 assert c.counter.count == 1
 "#
         );
-        let globals = PyModule::import(py, "__main__").unwrap().dict();
+        let globals = PyModule::import(py, "__main__")
+            .unwrap()
+            .dict()
+            .as_borrowed();
         globals.set_item("Counter", counter).unwrap();
-        py.run(source, Some(globals), None)
+        py.run_bound(source, Some(&globals), None)
             .map_err(|e| e.display(py))
             .unwrap();
     });