A bunch of new apps are coming to the Xbox 360 and Xbox One in the near future. Microsoft has a list of them on their website, but some of the highlights include Twitter, HBO Go, Showtime Anytime, NBA, NHL, and Vine.
About 45 apps will be coming, but not all of them will make it to the Xbox 360 or the Xbox One. There's a good variety coming down and you can see Microsoft highlight the Twitch integration in the video below.
If you're big into Twitter, the app seems to be pretty well baked in and should make you pretty happy.
No time table for when these apps will appear though.