We use gradle for building. The actual app is split into two, trello-app and trello-lib. Anything that can be done w/o Android like SQLite caching, API calls, etc., is done in trello-lib which is a plain Java library. It makes the dev cycle much faster since you can write a unit test and run it in a second.

We don't have CI setup yet. For the server we use something custom but will most likely be moving to Buildbot and with that we'll also setup Android CI.