diff --git a/axum/src/handler/into_extension_service.rs b/axum/src/handler/into_extension_service.rs
index 19e68281..1d9e54ef 100644
--- a/axum/src/handler/into_extension_service.rs
+++ b/axum/src/handler/into_extension_service.rs
@@ -58,6 +58,9 @@ where
         use futures_util::future::FutureExt;
 
         let handler = self.handler.clone();
+
+        // TODO(david): this is duplicated in `axum/src/routing/mod.rs`
+        // extract into helper function
         let State(state) = req
             .extensions()
             .get::<State<S>>()
diff --git a/axum/src/routing/method_routing.rs b/axum/src/routing/method_routing.rs
index 0a84e39b..e9cf34cf 100644
--- a/axum/src/routing/method_routing.rs
+++ b/axum/src/routing/method_routing.rs
@@ -672,6 +672,26 @@ impl<S, B, R> MethodRouter<S, B, Infallible, R> {
     }
 }
 
+impl<S, B> MethodRouter<S, B, Infallible, MissingState> {
+    pub(crate) fn change_state<S2>(self) -> MethodRouter<S2, B, Infallible, MissingState> {
+        debug_assert!(self.state.is_none());
+        MethodRouter {
+            state: None,
+            get: self.get,
+            head: self.head,
+            delete: self.delete,
+            options: self.options,
+            patch: self.patch,
+            post: self.post,
+            put: self.put,
+            trace: self.trace,
+            fallback: self.fallback,
+            allow_header: self.allow_header,
+            _marker: PhantomData,
+        }
+    }
+}
+
 impl<S, B> MethodRouter<S, B, Infallible, WithState>
 where
     B: Send + 'static,
@@ -1181,10 +1201,8 @@ where
 
         if req.extensions().get::<State<S>>().is_none() {
             // the `unwrap` is safe because `self.state` is always some if `R = WithState`, which it is
-            let prev = req
-                .extensions_mut()
+            req.extensions_mut()
                 .insert(State(state.as_ref().unwrap().clone()));
-            debug_assert!(prev.is_none());
         }
 
         call!(req, method, HEAD, head);
diff --git a/axum/src/routing/mod.rs b/axum/src/routing/mod.rs
index e3851c2b..8bb15948 100644
--- a/axum/src/routing/mod.rs
+++ b/axum/src/routing/mod.rs
@@ -21,7 +21,7 @@ use std::{
     sync::Arc,
     task::{Context, Poll},
 };
-use tower::{layer::layer_fn, ServiceBuilder};
+use tower::{layer::layer_fn, util::MapRequestLayer, ServiceBuilder};
 use tower_http::map_response_body::MapResponseBodyLayer;
 use tower_layer::Layer;
 use tower_service::Service;
@@ -168,13 +168,63 @@ where
             _marker: PhantomData,
         }
     }
+}
 
+impl<InnerState, B> Router<InnerState, B, MissingState>
+where
+    B: HttpBody + Send + 'static,
+{
     pub fn map_state<F, OuterState>(self, f: F) -> Router<OuterState, B, MissingState>
     where
-        // TODO(david): which Fn?
-        F: FnOnce(OuterState) -> S,
+        F: Fn(OuterState) -> InnerState + Clone + Send + Sync + 'static,
+        OuterState: Clone + Send + Sync + 'static,
+        InnerState: Send + Sync + 'static,
     {
-        todo!()
+        debug_assert!(self.state.is_none());
+
+        let routes = self
+            .routes
+            .into_iter()
+            .map(|(route_id, endpoint)| {
+                let endpoint = match endpoint {
+                    Endpoint::MethodRouter(method_router) => {
+                        // the state will be provided later in `<Router as Service>::call`, so its
+                        // safe to ignore that it hasn't been provided yet
+                        Endpoint::MethodRouter(method_router.change_state::<OuterState>())
+                    }
+                    Endpoint::Route(route) => Endpoint::Route(route),
+                };
+                (route_id, endpoint)
+            })
+            .collect();
+
+        Router {
+            state: None,
+            routes,
+            node: self.node,
+            fallback: self.fallback,
+            _marker: PhantomData,
+        }
+        .layer(MapRequestLayer::new(move |mut req: Request<_>| {
+            // TODO(david): this is duplicated in `axum/src/handler/into_extension_service.rs`
+            // extract into helper function
+            let State(outer_state) = req
+                .extensions()
+                .get::<State<OuterState>>()
+                .unwrap_or_else(|| {
+                    panic!(
+                        "no state of type `{}` was found. Please file an issue",
+                        std::any::type_name::<State<OuterState>>()
+                    )
+                })
+                .clone();
+
+            let inner_state = f(outer_state);
+
+            req.extensions_mut().insert(State(inner_state));
+
+            req
+        }))
     }
 }
 
diff --git a/axum/src/routing/tests/mod.rs b/axum/src/routing/tests/mod.rs
index 37c6dcd7..a00a5b7f 100644
--- a/axum/src/routing/tests/mod.rs
+++ b/axum/src/routing/tests/mod.rs
@@ -695,3 +695,8 @@ async fn extracting_state() {
     let res = client.get("/").send().await;
     assert_eq!(res.text().await, "foo");
 }
+
+#[tokio::test]
+async fn extracting_wrong_state_type_doesnt_compile() {
+    todo!()
+}
diff --git a/axum/src/routing/tests/nest.rs b/axum/src/routing/tests/nest.rs
index efb751ad..99fd5972 100644
--- a/axum/src/routing/tests/nest.rs
+++ b/axum/src/routing/tests/nest.rs
@@ -389,28 +389,35 @@ async fn nest_with_and_without_trailing() {
 #[tokio::test]
 async fn nesting_with_different_state() {
     #[derive(Clone)]
-    struct State {
+    struct AppState {
         inner: InnerState,
     }
 
     #[derive(Clone)]
-    struct InnerState {}
+    struct InnerState {
+        value: &'static str,
+    }
 
-    impl From<State> for InnerState {
-        fn from(state: State) -> Self {
+    impl From<AppState> for InnerState {
+        fn from(state: AppState) -> Self {
             state.inner
         }
     }
 
-    let inner_router = Router::<InnerState, Body, _>::new();
+    let inner_router = Router::<InnerState, Body, _>::new().route(
+        "/b",
+        get(|State(state): State<InnerState>| async move { state.value }),
+    );
 
-    let router_router = Router::<State, Body, _>::new()
-        .state(State {
-            inner: InnerState {},
-        })
-        .nest("/", inner_router.map_state(Into::into));
+    let app = Router::with_state(AppState {
+        inner: InnerState { value: "inner" },
+    })
+    .nest("/a", inner_router.map_state(Into::into));
 
-    todo!();
+    let client = TestClient::new(app);
+
+    let res = client.get("/a/b").send().await;
+    assert_eq!(res.text().await, "inner");
 }
 
 macro_rules! nested_route_test {