diff --git a/core/src/connection.rs b/core/src/connection.rs
index 3a8d54d04a1..425dc5d390d 100644
--- a/core/src/connection.rs
+++ b/core/src/connection.rs
@@ -230,14 +230,4 @@ impl ConnectedPoint {
             ConnectedPoint::Listener { send_back_addr, .. } => send_back_addr,
         }
     }
-
-    /// Modifies the address of the remote stored in this struct.
-    ///
-    /// For `Dialer`, this modifies `address`. For `Listener`, this modifies `send_back_addr`.
-    pub fn set_remote_address(&mut self, new_address: Multiaddr) {
-        match self {
-            ConnectedPoint::Dialer { address, .. } => *address = new_address,
-            ConnectedPoint::Listener { send_back_addr, .. } => *send_back_addr = new_address,
-        }
-    }
 }
diff --git a/core/src/muxing.rs b/core/src/muxing.rs
index 68e555e167f..8f16a1b086f 100644
--- a/core/src/muxing.rs
+++ b/core/src/muxing.rs
@@ -51,7 +51,6 @@
 //! implementation of `StreamMuxer` to control everything that happens on the wire.
 
 use futures::{task::Context, task::Poll, AsyncRead, AsyncWrite};
-use multiaddr::Multiaddr;
 use std::io;
 
 pub use self::boxed::StreamMuxerBox;
@@ -139,22 +138,14 @@ pub trait StreamMuxer {
 pub enum StreamMuxerEvent<T> {
     /// Remote has opened a new substream. Contains the substream in question.
     InboundSubstream(T),
-
-    /// Address to the remote has changed. The previous one is now obsolete.
-    ///
-    /// > **Note**: This can for example happen when using the QUIC protocol, where the two nodes
-    /// >           can change their IP address while retaining the same QUIC connection.
-    AddressChange(Multiaddr),
 }
 
 impl<T> StreamMuxerEvent<T> {
     /// If `self` is a [`StreamMuxerEvent::InboundSubstream`], returns the content. Otherwise
     /// returns `None`.
     pub fn into_inbound_substream(self) -> Option<T> {
-        if let StreamMuxerEvent::InboundSubstream(s) = self {
-            Some(s)
-        } else {
-            None
+        match self {
+            StreamMuxerEvent::InboundSubstream(stream) => Some(stream),
         }
     }
 
@@ -164,7 +155,6 @@ impl<T> StreamMuxerEvent<T> {
             StreamMuxerEvent::InboundSubstream(stream) => {
                 StreamMuxerEvent::InboundSubstream(map(stream))
             }
-            StreamMuxerEvent::AddressChange(addr) => StreamMuxerEvent::AddressChange(addr),
         }
     }
 }
diff --git a/core/src/muxing/boxed.rs b/core/src/muxing/boxed.rs
index f0e2ff10647..8345f747a0f 100644
--- a/core/src/muxing/boxed.rs
+++ b/core/src/muxing/boxed.rs
@@ -50,9 +50,6 @@ where
     ) -> Poll<Result<StreamMuxerEvent<Self::Substream>, Self::Error>> {
         let substream = match self.inner.poll_event(cx) {
             Poll::Pending => return Poll::Pending,
-            Poll::Ready(Ok(StreamMuxerEvent::AddressChange(a))) => {
-                return Poll::Ready(Ok(StreamMuxerEvent::AddressChange(a)))
-            }
             Poll::Ready(Ok(StreamMuxerEvent::InboundSubstream(s))) => s,
             Poll::Ready(Err(err)) => return Poll::Ready(Err(err.into())),
         };
diff --git a/muxers/mplex/src/lib.rs b/muxers/mplex/src/lib.rs
index 80b1db16481..8f692ca4a68 100644
--- a/muxers/mplex/src/lib.rs
+++ b/muxers/mplex/src/lib.rs
@@ -75,9 +75,6 @@ where
 }
 
 /// Multiplexer. Implements the `StreamMuxer` trait.
-///
-/// This implementation isn't capable of detecting when the underlying socket changes its address,
-/// and no [`StreamMuxerEvent::AddressChange`] event is ever emitted.
 pub struct Multiplex<C> {
     io: Arc<Mutex<io::Multiplexed<C>>>,
 }
diff --git a/muxers/yamux/src/lib.rs b/muxers/yamux/src/lib.rs
index 8eb6fb3e895..f74226b3049 100644
--- a/muxers/yamux/src/lib.rs
+++ b/muxers/yamux/src/lib.rs
@@ -97,7 +97,6 @@ where
 
 pub type YamuxResult<T> = Result<T, YamuxError>;
 
-/// > **Note**: This implementation never emits [`StreamMuxerEvent::AddressChange`] events.
 impl<S> StreamMuxer for Yamux<S>
 where
     S: Stream<Item = Result<yamux::Stream, YamuxError>> + Unpin,
diff --git a/protocols/autonat/src/behaviour.rs b/protocols/autonat/src/behaviour.rs
index 86c65bb3416..58102932cbe 100644
--- a/protocols/autonat/src/behaviour.rs
+++ b/protocols/autonat/src/behaviour.rs
@@ -383,29 +383,6 @@ impl NetworkBehaviour for Behaviour {
         }
     }
 
-    fn inject_address_change(
-        &mut self,
-        peer: &PeerId,
-        conn: &ConnectionId,
-        old: &ConnectedPoint,
-        new: &ConnectedPoint,
-    ) {
-        self.inner.inject_address_change(peer, conn, old, new);
-
-        if old.is_relayed() && new.is_relayed() {
-            return;
-        }
-        let connections = self.connected.get_mut(peer).expect("Peer is connected.");
-        let addr = new.get_remote_address();
-        let observed_addr =
-            if !new.is_relayed() && (!self.config.only_global_ips || addr.is_global_ip()) {
-                Some(addr.clone())
-            } else {
-                None
-            };
-        connections.insert(*conn, observed_addr);
-    }
-
     fn inject_new_listen_addr(&mut self, id: ListenerId, addr: &Multiaddr) {
         self.inner.inject_new_listen_addr(id, addr);
         self.as_client().on_new_address();
diff --git a/swarm/CHANGELOG.md b/swarm/CHANGELOG.md
index 1a633edc534..75585133b1d 100644
--- a/swarm/CHANGELOG.md
+++ b/swarm/CHANGELOG.md
@@ -1,6 +1,10 @@
 # 0.37.0 [unreleased]
 
 - Update to `libp2p-core` `v0.34.0`.
+- Deprecate `NetworkBehaviour::inject_address_change` and
+  `Connectionhandler::inject_address_change`. See [PR XXXX].
+
+[PR XXXX]: https://github.com/libp2p/rust-libp2p/pull/XXXX
 
 # 0.36.2 [unreleased]
 
diff --git a/swarm/src/behaviour.rs b/swarm/src/behaviour.rs
index d09427fbc6b..f250d38c729 100644
--- a/swarm/src/behaviour.rs
+++ b/swarm/src/behaviour.rs
@@ -232,6 +232,7 @@ pub trait NetworkBehaviour: 'static {
     }
 
     /// Informs the behaviour that the [`ConnectedPoint`] of an existing connection has changed.
+    #[deprecated(since = "0.37.0", note = "This function will no longer be called.")]
     fn inject_address_change(
         &mut self,
         _: &PeerId,
diff --git a/swarm/src/behaviour/either.rs b/swarm/src/behaviour/either.rs
index 479534f6a8f..9f01c451460 100644
--- a/swarm/src/behaviour/either.rs
+++ b/swarm/src/behaviour/either.rs
@@ -107,19 +107,6 @@ where
         }
     }
 
-    fn inject_address_change(
-        &mut self,
-        peer_id: &PeerId,
-        connection: &ConnectionId,
-        old: &ConnectedPoint,
-        new: &ConnectedPoint,
-    ) {
-        match self {
-            Either::Left(a) => a.inject_address_change(peer_id, connection, old, new),
-            Either::Right(b) => b.inject_address_change(peer_id, connection, old, new),
-        }
-    }
-
     fn inject_event(
         &mut self,
         peer_id: PeerId,
diff --git a/swarm/src/behaviour/toggle.rs b/swarm/src/behaviour/toggle.rs
index 25183b932c7..b5de3a9494c 100644
--- a/swarm/src/behaviour/toggle.rs
+++ b/swarm/src/behaviour/toggle.rs
@@ -126,18 +126,6 @@ where
         }
     }
 
-    fn inject_address_change(
-        &mut self,
-        peer_id: &PeerId,
-        connection: &ConnectionId,
-        old: &ConnectedPoint,
-        new: &ConnectedPoint,
-    ) {
-        if let Some(inner) = self.inner.as_mut() {
-            inner.inject_address_change(peer_id, connection, old, new)
-        }
-    }
-
     fn inject_event(
         &mut self,
         peer_id: PeerId,
@@ -345,12 +333,6 @@ where
             .inject_event(event)
     }
 
-    fn inject_address_change(&mut self, addr: &Multiaddr) {
-        if let Some(inner) = self.inner.as_mut() {
-            inner.inject_address_change(addr)
-        }
-    }
-
     fn inject_dial_upgrade_error(
         &mut self,
         info: Self::OutboundOpenInfo,
diff --git a/swarm/src/connection.rs b/swarm/src/connection.rs
index e53701699e2..432acc96bca 100644
--- a/swarm/src/connection.rs
+++ b/swarm/src/connection.rs
@@ -59,8 +59,6 @@ pub struct Connected {
 pub enum Event<T> {
     /// Event generated by the [`ConnectionHandler`].
     Handler(T),
-    /// Address of the remote has changed.
-    AddressChange(Multiaddr),
 }
 
 /// A multiplexed connection to a peer with an associated [`ConnectionHandler`].
@@ -166,10 +164,6 @@ where
                     self.handler.inject_substream(substream, endpoint);
                     continue;
                 }
-                Poll::Ready(Ok(SubstreamEvent::AddressChange(address))) => {
-                    self.handler.inject_address_change(&address);
-                    return Poll::Ready(Ok(Event::AddressChange(address)));
-                }
                 Poll::Ready(Err(err)) => return Poll::Ready(Err(ConnectionError::IO(err))),
             }
 
diff --git a/swarm/src/connection/handler_wrapper.rs b/swarm/src/connection/handler_wrapper.rs
index 77eb1d79bbf..da040d69178 100644
--- a/swarm/src/connection/handler_wrapper.rs
+++ b/swarm/src/connection/handler_wrapper.rs
@@ -32,7 +32,6 @@ use instant::Instant;
 use libp2p_core::{
     muxing::SubstreamBox,
     upgrade::{self, InboundUpgradeApply, OutboundUpgradeApply, UpgradeError},
-    Multiaddr,
 };
 use libp2p_core::{ConnectedPoint, PeerId};
 use std::{error, fmt, pin::Pin, task::Context, task::Poll, time::Duration};
@@ -317,10 +316,6 @@ where
         self.handler.inject_event(event);
     }
 
-    pub fn inject_address_change(&mut self, new_address: &Multiaddr) {
-        self.handler.inject_address_change(new_address);
-    }
-
     fn handle_connection_handler_event(
         &mut self,
         handler_event: ConnectionHandlerEvent<
diff --git a/swarm/src/connection/pool.rs b/swarm/src/connection/pool.rs
index 10fc29a8120..2aa24240219 100644
--- a/swarm/src/connection/pool.rs
+++ b/swarm/src/connection/pool.rs
@@ -236,16 +236,6 @@ where
         /// The produced event.
         event: THandlerOutEvent<THandler>,
     },
-
-    /// The connection to a node has changed its address.
-    AddressChange {
-        id: ConnectionId,
-        peer_id: PeerId,
-        /// The new endpoint.
-        new_endpoint: ConnectedPoint,
-        /// The old endpoint.
-        old_endpoint: ConnectedPoint,
-    },
 }
 
 impl<THandler, TTrans> Pool<THandler, TTrans>
@@ -542,29 +532,6 @@ where
             Poll::Ready(Some(task::EstablishedConnectionEvent::Notify { id, peer_id, event })) => {
                 return Poll::Ready(PoolEvent::ConnectionEvent { peer_id, id, event });
             }
-            Poll::Ready(Some(task::EstablishedConnectionEvent::AddressChange {
-                id,
-                peer_id,
-                new_address,
-            })) => {
-                let connection = self
-                    .established
-                    .get_mut(&peer_id)
-                    .expect("Receive `AddressChange` event for established peer.")
-                    .get_mut(&id)
-                    .expect("Receive `AddressChange` event from established connection");
-                let mut new_endpoint = connection.endpoint.clone();
-                new_endpoint.set_remote_address(new_address);
-                let old_endpoint =
-                    std::mem::replace(&mut connection.endpoint, new_endpoint.clone());
-
-                return Poll::Ready(PoolEvent::AddressChange {
-                    peer_id,
-                    id,
-                    new_endpoint,
-                    old_endpoint,
-                });
-            }
             Poll::Ready(Some(task::EstablishedConnectionEvent::Closed {
                 id,
                 peer_id,
diff --git a/swarm/src/connection/pool/task.rs b/swarm/src/connection/pool/task.rs
index 866049e50da..06c69f40f15 100644
--- a/swarm/src/connection/pool/task.rs
+++ b/swarm/src/connection/pool/task.rs
@@ -73,12 +73,6 @@ where
 
 #[derive(Debug)]
 pub enum EstablishedConnectionEvent<THandler: ConnectionHandler> {
-    /// A node we are connected to has changed its address.
-    AddressChange {
-        id: ConnectionId,
-        peer_id: PeerId,
-        new_address: Multiaddr,
-    },
     /// Notify the manager of an event from the connection.
     Notify {
         id: ConnectionId,
@@ -225,15 +219,6 @@ pub async fn new_for_established_connection<THandler>(
                             })
                             .await;
                     }
-                    Ok(connection::Event::AddressChange(new_address)) => {
-                        let _ = events
-                            .send(EstablishedConnectionEvent::AddressChange {
-                                id: connection_id,
-                                peer_id,
-                                new_address,
-                            })
-                            .await;
-                    }
                     Err(error) => {
                         command_receiver.close();
                         let (handler, _closing_muxer) = connection.close();
diff --git a/swarm/src/connection/substream.rs b/swarm/src/connection/substream.rs
index 50714585366..d0c9c564c34 100644
--- a/swarm/src/connection/substream.rs
+++ b/swarm/src/connection/substream.rs
@@ -19,7 +19,6 @@
 // DEALINGS IN THE SOFTWARE.
 
 use futures::prelude::*;
-use libp2p_core::multiaddr::Multiaddr;
 use libp2p_core::muxing::{StreamMuxer, StreamMuxerEvent};
 use smallvec::SmallVec;
 use std::sync::Arc;
@@ -75,12 +74,6 @@ where
         /// destroyed or `close_graceful` is called.
         substream: TMuxer::Substream,
     },
-
-    /// Address to the remote has changed. The previous one is now obsolete.
-    ///
-    /// > **Note**: This can for example happen when using the QUIC protocol, where the two nodes
-    /// >           can change their IP address while retaining the same QUIC connection.
-    AddressChange(Multiaddr),
 }
 
 /// Identifier for a substream being opened.
@@ -140,9 +133,6 @@ where
             Poll::Ready(Ok(StreamMuxerEvent::InboundSubstream(substream))) => {
                 return Poll::Ready(Ok(SubstreamEvent::InboundSubstream { substream }));
             }
-            Poll::Ready(Ok(StreamMuxerEvent::AddressChange(addr))) => {
-                return Poll::Ready(Ok(SubstreamEvent::AddressChange(addr)))
-            }
             Poll::Ready(Err(err)) => return Poll::Ready(Err(err.into())),
             Poll::Pending => {}
         }
@@ -243,10 +233,6 @@ where
                 .field("user_data", user_data)
                 .field("substream", substream)
                 .finish(),
-            SubstreamEvent::AddressChange(address) => f
-                .debug_struct("SubstreamEvent::AddressChange")
-                .field("address", address)
-                .finish(),
         }
     }
 }
diff --git a/swarm/src/handler.rs b/swarm/src/handler.rs
index 2a301b70889..8fe307184f9 100644
--- a/swarm/src/handler.rs
+++ b/swarm/src/handler.rs
@@ -136,6 +136,7 @@ pub trait ConnectionHandler: Send + 'static {
     fn inject_event(&mut self, event: Self::InEvent);
 
     /// Notifies the handler of a change in the address of the remote.
+    #[deprecated(since = "0.37.0", note = "This handler will no longer be called.")]
     fn inject_address_change(&mut self, _new_address: &Multiaddr) {}
 
     /// Indicates to the handler that upgrading an outbound substream to the given protocol has failed.
diff --git a/swarm/src/handler/either.rs b/swarm/src/handler/either.rs
index 21d386ec56a..a29ce915312 100644
--- a/swarm/src/handler/either.rs
+++ b/swarm/src/handler/either.rs
@@ -26,7 +26,7 @@ use crate::upgrade::{InboundUpgradeSend, OutboundUpgradeSend, SendWrapper};
 use either::Either;
 use libp2p_core::either::{EitherError, EitherOutput};
 use libp2p_core::upgrade::{EitherUpgrade, UpgradeError};
-use libp2p_core::{ConnectedPoint, Multiaddr, PeerId};
+use libp2p_core::{ConnectedPoint, PeerId};
 use std::task::{Context, Poll};
 
 pub enum IntoEitherHandler<L, R> {
@@ -134,13 +134,6 @@ where
         }
     }
 
-    fn inject_address_change(&mut self, addr: &Multiaddr) {
-        match self {
-            Either::Left(handler) => handler.inject_address_change(addr),
-            Either::Right(handler) => handler.inject_address_change(addr),
-        }
-    }
-
     fn inject_dial_upgrade_error(
         &mut self,
         info: Self::OutboundOpenInfo,
diff --git a/swarm/src/handler/map_in.rs b/swarm/src/handler/map_in.rs
index a209225045e..18e2b4c57de 100644
--- a/swarm/src/handler/map_in.rs
+++ b/swarm/src/handler/map_in.rs
@@ -23,7 +23,6 @@ use crate::handler::{
     SubstreamProtocol,
 };
 use crate::upgrade::{InboundUpgradeSend, OutboundUpgradeSend};
-use libp2p_core::Multiaddr;
 use std::{fmt::Debug, marker::PhantomData, task::Context, task::Poll};
 
 /// Wrapper around a protocol handler that turns the input event into something else.
@@ -86,10 +85,6 @@ where
         }
     }
 
-    fn inject_address_change(&mut self, addr: &Multiaddr) {
-        self.inner.inject_address_change(addr)
-    }
-
     fn inject_dial_upgrade_error(
         &mut self,
         info: Self::OutboundOpenInfo,
diff --git a/swarm/src/handler/map_out.rs b/swarm/src/handler/map_out.rs
index 2eb0c2f9bdc..43c7954eeeb 100644
--- a/swarm/src/handler/map_out.rs
+++ b/swarm/src/handler/map_out.rs
@@ -23,7 +23,6 @@ use crate::handler::{
     SubstreamProtocol,
 };
 use crate::upgrade::{InboundUpgradeSend, OutboundUpgradeSend};
-use libp2p_core::Multiaddr;
 use std::fmt::Debug;
 use std::task::{Context, Poll};
 
@@ -79,10 +78,6 @@ where
         self.inner.inject_event(event)
     }
 
-    fn inject_address_change(&mut self, addr: &Multiaddr) {
-        self.inner.inject_address_change(addr)
-    }
-
     fn inject_dial_upgrade_error(
         &mut self,
         info: Self::OutboundOpenInfo,
diff --git a/swarm/src/handler/multi.rs b/swarm/src/handler/multi.rs
index f7e4d7ed1b4..0b9410f6e8c 100644
--- a/swarm/src/handler/multi.rs
+++ b/swarm/src/handler/multi.rs
@@ -29,7 +29,7 @@ use crate::upgrade::{InboundUpgradeSend, OutboundUpgradeSend, UpgradeInfoSend};
 use crate::NegotiatedSubstream;
 use futures::{future::BoxFuture, prelude::*};
 use libp2p_core::upgrade::{NegotiationError, ProtocolError, ProtocolName, UpgradeError};
-use libp2p_core::{ConnectedPoint, Multiaddr, PeerId};
+use libp2p_core::{ConnectedPoint, PeerId};
 use rand::Rng;
 use std::{
     cmp,
@@ -155,12 +155,6 @@ where
         }
     }
 
-    fn inject_address_change(&mut self, addr: &Multiaddr) {
-        for h in self.handlers.values_mut() {
-            h.inject_address_change(addr)
-        }
-    }
-
     fn inject_dial_upgrade_error(
         &mut self,
         (key, arg): Self::OutboundOpenInfo,
diff --git a/swarm/src/handler/select.rs b/swarm/src/handler/select.rs
index 70a6f3c26f6..92573bfb86d 100644
--- a/swarm/src/handler/select.rs
+++ b/swarm/src/handler/select.rs
@@ -27,7 +27,7 @@ use crate::upgrade::{InboundUpgradeSend, OutboundUpgradeSend, SendWrapper};
 use libp2p_core::{
     either::{EitherError, EitherOutput},
     upgrade::{EitherUpgrade, NegotiationError, ProtocolError, SelectUpgrade, UpgradeError},
-    ConnectedPoint, Multiaddr, PeerId,
+    ConnectedPoint, PeerId,
 };
 use std::{cmp, task::Context, task::Poll};
 
@@ -169,11 +169,6 @@ where
         }
     }
 
-    fn inject_address_change(&mut self, new_address: &Multiaddr) {
-        self.proto1.inject_address_change(new_address);
-        self.proto2.inject_address_change(new_address)
-    }
-
     fn inject_dial_upgrade_error(
         &mut self,
         info: Self::OutboundOpenInfo,
diff --git a/swarm/src/lib.rs b/swarm/src/lib.rs
index c5ef1b0aa88..a4dcd3c97b9 100644
--- a/swarm/src/lib.rs
+++ b/swarm/src/lib.rs
@@ -810,21 +810,6 @@ where
                     self.behaviour.inject_event(peer_id, id, event);
                 }
             }
-            PoolEvent::AddressChange {
-                peer_id,
-                id,
-                new_endpoint,
-                old_endpoint,
-            } => {
-                if !self.banned_peer_connections.contains(&id) {
-                    self.behaviour.inject_address_change(
-                        &peer_id,
-                        &id,
-                        &old_endpoint,
-                        &new_endpoint,
-                    );
-                }
-            }
         }
 
         None