Looper is a time travel movie of the “self-healing timeline” mechanic (a-la Back To The Future, although Looper “fixes” itself faster and changes to the time stream can be observed and remembered by everybody affected by them). As a result of this, and a few other issues, it suffers from a handful of plotholes and internal inconsistencies: however, it’s still an enormously fun film that I’d recommend that you see.
Looper is the second-best of all three movies that feature Bruce Willis travelling back in time and encountering a younger version of himself – and now it’s going to bug you until you work out what the other two are.