In reply to drchop:
I think it's worth distinguishing between the app itself and the crags that you've downloaded via the app.
The app itself will typically auto-update when new versions are released (unless this is something you have disabled on your phone)
as Graham said, the topos on the app won't update unless you specifically tell it to. I've attached a pic of what the update button looks like. These are currently pending an update for me because I had the old topos downloaded, then the new version of peak bouldering has recently been released which means new versions of those topos are available.