The Polkadot-Kusama bridge has gone live recently. GRANDPA light clients running on the Polkadot and Kusama BridgeHubs have been initialized and are currently being synced in real time by a permissionless relayer run by Parity.
The consensus proof logic (light client), parachain head proof logic, and message proof logic are all running on the BridgeHub runtime midchain, which is completely controlled by Polkadot/Kusama governance. This means that Polkadot and Kusama are currently tracking each other's chain progress and importing messages from each other in a trustless manner.
Initially, the bridge has one open "channel" serving XCM communication between the Polkadot Asset Hub and the Kusama Asset Hub. However, it also supports opening other channels between other parachains on both sides of the bridge.
The PAH <> KAH (Polkadot Asset Hub <> Kusama Asset Hub) bridge channel basically supports any XCM, but currently, the PAH and KAH runtimes have been configured to only accept DOT and KSM transfers back and forth. Soon, they will also allow the transfer of stablecoins; after that, they will be open to any asset owner, allowing them to register assets as ForeignAssets on the remote asset center, just like on the local asset center. (PolkaWorld)