Kodi, formerly XBMC, has been available on Android in its revamped form since early April. But if you wanted to get your hands on it, you had to join either the alpha or beta groups on Google+, then register on the Play Store as a tester. Not so today: it looks like the developers have opened up the beta Play Store listing for one and all, and you can download it directly to your phone, tablet, or Android TV set-top box.
This build is based on the version 15 beta 2 code, the same "Isengard" open source release available on Windows, OS X, and iOS. There are too many improvements since beta 1 to list here, but the big additions are a revamped storage framework for Android and enhancements to the fast forward and rewind functions. The full changelog can be found at Kodi.tv.
The alpha version is still available via the Google+ communities method - head to this page to sign up then this page to opt-in if you're interested in testing out bleeding edge features. All APK files are also available on the primary Kodi download page, though you may need to update them manually if you install the app outside of the Play Store.