There are now several Apple Live Streaming Software and apps that are compatible with Apple TV. Hulu with Live TV, Sling TV, etc., are some of the streaming services that can be used for live streaming your favorite program.
The AirBrowser app enables Apple TV to function as a desktop browser. The method is different from the standard screen mirroring feature. You can use the iOS device as a remote while streaming the playback video on your TV.
Internet videos can be streamed directly using the AirPlay feature. The Safari browser can be casted on your Apple TV, or you can Airplay YouTube-like apps to watch Internet videos on Apple TV.