diff --git a/pyo3-macros-backend/src/method.rs b/pyo3-macros-backend/src/method.rs
index 7ea65899850..8dcbd3118b6 100644
--- a/pyo3-macros-backend/src/method.rs
+++ b/pyo3-macros-backend/src/method.rs
@@ -449,7 +449,23 @@ impl<'a> FnSpec<'a> {
         let rust_call = |args: Vec<TokenStream>| {
             let mut call = quote! { function(#self_arg #(#args),*) };
             if self.asyncness.is_some() {
-                call = quote! { _pyo3::impl_::coroutine::wrap_future(#call) };
+                let python_name = &self.python_name;
+                let qualname = match cls {
+                    Some(cls) => quote! {
+                        Some(_pyo3::impl_::coroutine::method_coroutine_qualname::<#cls>(py, stringify!(#python_name)))
+                    },
+                    None => quote! {
+                        _pyo3::impl_::coroutine::coroutine_qualname(py, py.from_borrowed_ptr_or_opt::<_pyo3::types::PyModule>(_slf), stringify!(#python_name))
+                    },
+                };
+                call = quote! {{
+                    let future = #call;
+                    _pyo3::impl_::coroutine::new_coroutine(
+                        Some(_pyo3::impl_::coroutine::coroutine_name(py, stringify!(#python_name))),
+                        #qualname,
+                        async move { _pyo3::impl_::wrap::OkWrap::wrap_no_gil(future.await) }
+                    )
+                }};
             }
             quotes::map_result_into_ptr(quotes::ok_wrap(call))
         };
diff --git a/src/coroutine.rs b/src/coroutine.rs
index a530184a1c3..6705bfd56a5 100644
--- a/src/coroutine.rs
+++ b/src/coroutine.rs
@@ -14,10 +14,10 @@ use pyo3_macros::{pyclass, pymethods};
 
 use crate::{
     coroutine::waker::AsyncioWaker,
-    exceptions::{PyRuntimeError, PyStopIteration},
+    exceptions::{PyAttributeError, PyRuntimeError, PyRuntimeWarning, PyStopIteration},
     panic::PanicException,
     pyclass::IterNextOutput,
-    types::PyIterator,
+    types::{PyIterator, PyString},
     IntoPy, Py, PyAny, PyErr, PyObject, PyResult, Python,
 };
 
@@ -30,6 +30,8 @@ type FutureOutput = Result<PyResult<PyObject>, Box<dyn Any + Send>>;
 /// Python coroutine wrapping a [`Future`].
 #[pyclass(crate = "crate")]
 pub struct Coroutine {
+    name: Option<Py<PyString>>,
+    qualname: Option<Py<PyString>>,
     future: Option<Pin<Box<dyn Future<Output = FutureOutput> + Send>>>,
     waker: Option<Arc<AsyncioWaker>>,
 }
@@ -41,7 +43,11 @@ impl Coroutine {
     /// (should always be `None` anyway).
     ///
     /// `Coroutine `throw` drop the wrapped future and reraise the exception passed
-    pub(crate) fn from_future<F, T, E>(future: F) -> Self
+    pub(crate) fn new<F, T, E>(
+        name: Option<Py<PyString>>,
+        mut qualname: Option<Py<PyString>>,
+        future: F,
+    ) -> Self
     where
         F: Future<Output = Result<T, E>> + Send + 'static,
         T: IntoPy<PyObject>,
@@ -52,7 +58,10 @@ impl Coroutine {
             // SAFETY: GIL is acquired when future is polled (see `Coroutine::poll`)
             Ok(obj.into_py(unsafe { Python::assume_gil_acquired() }))
         };
+        qualname = qualname.or_else(|| name.clone());
         Self {
+            name,
+            qualname,
             future: Some(Box::pin(panic::AssertUnwindSafe(wrap).catch_unwind())),
             waker: None,
         }
@@ -113,6 +122,20 @@ pub(crate) fn iter_result(result: IterNextOutput<PyObject, PyObject>) -> PyResul
 
 #[pymethods(crate = "crate")]
 impl Coroutine {
+    #[getter]
+    fn __name__(&self) -> PyResult<Py<PyString>> {
+        self.name
+            .clone()
+            .ok_or_else(|| PyAttributeError::new_err("__name__"))
+    }
+
+    #[getter]
+    fn __qualname__(&self) -> PyResult<Py<PyString>> {
+        self.qualname
+            .clone()
+            .ok_or_else(|| PyAttributeError::new_err("__qualname__"))
+    }
+
     fn send(&mut self, py: Python<'_>, _value: &PyAny) -> PyResult<PyObject> {
         iter_result(self.poll(py, None)?)
     }
@@ -135,3 +158,21 @@ impl Coroutine {
         self.poll(py, None)
     }
 }
+
+impl Drop for Coroutine {
+    fn drop(&mut self) {
+        if self.future.is_some() {
+            Python::with_gil(|gil| {
+                let qualname = self
+                    .qualname
+                    .as_ref()
+                    .map_or(Ok("<coroutine>"), |n| n.as_ref(gil).to_str())
+                    .unwrap();
+                let message = format!("coroutine {qualname} was never awaited");
+                PyErr::warn(gil, gil.get_type::<PyRuntimeWarning>(), &message, 2)
+                    .expect("warning error");
+                self.poll(gil, None).expect("coroutine close error");
+            })
+        }
+    }
+}
diff --git a/src/impl_/coroutine.rs b/src/impl_/coroutine.rs
index 843c42f169a..fe23e7c41bd 100644
--- a/src/impl_/coroutine.rs
+++ b/src/impl_/coroutine.rs
@@ -1,19 +1,41 @@
-use crate::coroutine::Coroutine;
-use crate::impl_::wrap::OkWrap;
-use crate::{IntoPy, PyErr, PyObject, Python};
 use std::future::Future;
 
-/// Used to wrap the result of async `#[pyfunction]` and `#[pymethods]`.
-pub fn wrap_future<F, R, T>(future: F) -> Coroutine
+use crate::{
+    coroutine::Coroutine,
+    types::{PyModule, PyString},
+    IntoPy, Py, PyClass, PyErr, PyObject, Python,
+};
+
+pub fn new_coroutine<F, T, E>(
+    name: Option<Py<PyString>>,
+    qualname: Option<Py<PyString>>,
+    future: F,
+) -> Coroutine
 where
-    F: Future<Output = R> + Send + 'static,
-    R: OkWrap<T>,
+    F: Future<Output = Result<T, E>> + Send + 'static,
     T: IntoPy<PyObject>,
-    PyErr: From<R::Error>,
+    PyErr: From<E>,
 {
-    let future = async move {
-        // SAFETY: GIL is acquired when future is polled (see `Coroutine::poll`)
-        future.await.wrap(unsafe { Python::assume_gil_acquired() })
+    Coroutine::new(name, qualname, future)
+}
+
+pub fn coroutine_name(py: Python<'_>, name: &str) -> Py<PyString> {
+    PyString::new(py, name).into()
+}
+
+pub unsafe fn coroutine_qualname(
+    py: Python<'_>,
+    module: Option<&PyModule>,
+    name: &str,
+) -> Option<Py<PyString>> {
+    Some(PyString::new(py, &format!("{}.{name}", module?.name().ok()?)).into())
+}
+
+pub fn method_coroutine_qualname<T: PyClass>(py: Python<'_>, name: &str) -> Py<PyString> {
+    let class = T::NAME;
+    let qualname = match T::MODULE {
+        Some(module) => format!("{module}.{class}.{name}"),
+        None => format!("{class}.{name}"),
     };
-    Coroutine::from_future(future)
+    PyString::new(py, &qualname).into()
 }
diff --git a/src/impl_/wrap.rs b/src/impl_/wrap.rs
index a73e3597302..08fab47a7ba 100644
--- a/src/impl_/wrap.rs
+++ b/src/impl_/wrap.rs
@@ -20,6 +20,7 @@ impl<T> SomeWrap<Option<T>> for Option<T> {
 /// Used to wrap the result of `#[pyfunction]` and `#[pymethods]`.
 pub trait OkWrap<T> {
     type Error;
+    fn wrap_no_gil(self) -> Result<T, Self::Error>;
     fn wrap(self, py: Python<'_>) -> Result<Py<PyAny>, Self::Error>;
 }
 
@@ -30,6 +31,9 @@ where
     T: IntoPy<PyObject>,
 {
     type Error = PyErr;
+    fn wrap_no_gil(self) -> Result<T, Self::Error> {
+        Ok(self)
+    }
     fn wrap(self, py: Python<'_>) -> PyResult<Py<PyAny>> {
         Ok(self.into_py(py))
     }
@@ -40,6 +44,9 @@ where
     T: IntoPy<PyObject>,
 {
     type Error = E;
+    fn wrap_no_gil(self) -> Result<T, Self::Error> {
+        self
+    }
     fn wrap(self, py: Python<'_>) -> Result<Py<PyAny>, Self::Error> {
         self.map(|o| o.into_py(py))
     }
diff --git a/tests/test_coroutine.rs b/tests/test_coroutine.rs
index a24d6bbd142..5ae1f58145a 100644
--- a/tests/test_coroutine.rs
+++ b/tests/test_coroutine.rs
@@ -1,7 +1,9 @@
 #![cfg(feature = "macros")]
+use std::ops::Deref;
 use std::{task::Poll, thread, time::Duration};
 
 use futures::{channel::oneshot, future::poll_fn};
+use pyo3::types::IntoPyDict;
 use pyo3::{prelude::*, py_run};
 
 #[path = "../src/tests/common.rs"]
@@ -29,6 +31,71 @@ fn noop_coroutine() {
     })
 }
 
+#[test]
+fn test_coroutine_qualname() {
+    #[pyfunction]
+    async fn my_fn() {}
+    #[pyclass]
+    struct MyClass;
+    #[pymethods]
+    impl MyClass {
+        #[new]
+        fn new() -> Self {
+            Self
+        }
+        // TODO use &self when possible
+        async fn my_method(_self: Py<Self>) {}
+        // TODO uncomment when https://github.com/PyO3/pyo3/pull/3587 is merged
+        // #[classmethod]
+        // async fn my_classmethod(_cls: Py<PyType>) {}
+        #[staticmethod]
+        async fn my_staticmethod() {}
+    }
+    #[pyclass(module = "my_module")]
+    struct MyClassWithModule;
+    #[pymethods]
+    impl MyClassWithModule {
+        #[new]
+        fn new() -> Self {
+            Self
+        }
+        // TODO use &self when possible
+        async fn my_method(_self: Py<Self>) {}
+        // TODO uncomment when https://github.com/PyO3/pyo3/pull/3587 is merged
+        // #[classmethod]
+        // async fn my_classmethod(_cls: Py<PyType>) {}
+        #[staticmethod]
+        async fn my_staticmethod() {}
+    }
+    Python::with_gil(|gil| {
+        let test = r#"
+        for coro, name, qualname in [
+            (my_fn(), "my_fn", "my_fn"),
+            (my_fn_with_module(), "my_fn", "my_module.my_fn"),
+            (MyClass().my_method(), "my_method", "MyClass.my_method"),
+            #(MyClass().my_classmethod(), "my_classmethod", "MyClass.my_classmethod"),
+            (MyClass.my_staticmethod(), "my_staticmethod", "MyClass.my_staticmethod"),
+            (MyClassWithModule().my_method(), "my_method", "my_module.MyClassWithModule.my_method"),
+            #(MyClassWithModule().my_classmethod(), "my_classmethod", "my_module.MyClassWithModule.my_classmethod"),
+            (MyClassWithModule.my_staticmethod(), "my_staticmethod", "my_module.MyClassWithModule.my_staticmethod"),
+        ]:
+            assert coro.__name__ == name and coro.__qualname__ == qualname
+        "#;
+        let my_module = PyModule::new(gil, "my_module").unwrap();
+        let locals = [
+            ("my_fn", wrap_pyfunction!(my_fn, gil).unwrap().deref()),
+            (
+                "my_fn_with_module",
+                wrap_pyfunction!(my_fn, my_module).unwrap(),
+            ),
+            ("MyClass", gil.get_type::<MyClass>()),
+            ("MyClassWithModule", gil.get_type::<MyClassWithModule>()),
+        ]
+        .into_py_dict(gil);
+        py_run!(gil, *locals, &handle_windows(test));
+    })
+}
+
 #[test]
 fn sleep_0_like_coroutine() {
     #[pyfunction]