From the official Twitch weblog:
You’ve been asking for it, we’ve been working on it, and it’s finally here: VODs on mobile! You will now be able to watch highlights and past broadcasts from all Twitch Partners and a growing number of broadcasters whose videos are HLS enabled.
I don’t watch Twitch as often as I used to, but I’m glad they finally added the one feature I wanted most. It’s kind of amazing that it took them this long.
(Via 9 to 5 Mac.)