Joseph Gordon-Levitt plays a very special kind of assassin in 2044. As he explains, time travel hasn't been invented yet, but 30 years in the future it has been. It's immediately outlawed, and only the most powerful criminal organizations have it. They use it to kill those they want to get rid of. Apparently something about how hard it is to dispose of a body in the future (don't think to hard about it, trying to explicate its logic is where the movie is at its weakest.) So a guy is sent back in time to a designated spot (near a field in Kansas) with a bag over his head and silver bars tied to his body. The assassin or "Looper" kills him right away, disposes of the body, and pockets the silver as payment. However, their knowledge of time travel is also dangerous to the mob, so eventually their future self is sent back to be assassinated. It's a big payday (gold instead of silver) and your retirement party, but also proof that you'll be dead in 30 years. Killing your future self is known as "closing your loop" and hence they're called loopers.
There's also some stuff about telekinesis that's introduced early on, forgotten for an hour, and then of course is massively important in the end. That part is pretty telegraphed.
So let me deal with the time travel logic first, since I'm kind of a time travel geek. It uses essentially Back to the Future rules, where changes in the past rewrite the future, even for characters who have travelled to the past from a different future. But instead of Marty McFly slowly dissolving away in front of his own eyes, time travelling characters can lose fingers or gain scars as their younger selves sustain injuries (in fact, carving a message onto your arm is a way to send that message in scar form to your future self.) This is not Feynman-diagrammable with closed time-like loops. I.e., it does not represent a single, self-consistent universe (few movies do, with my favorite examples being TIMECRIMES and 12 MONKEYS) but rather a multiple possible universes interpretation. This already makes me discount it a bit as "not a real time travel movie."
However, the time travel logic isn't what's important. As I said, explicating the logic is its weakest point. What is strong is how it presents a world where the hero character can directly see the 30-year repercussions of his actions. A world where the older version of himself (oh yeah, played by Bruce Willis) can actually sit his younger self down and tell him how stupid he's being (something I think everyone dreams of doing once they've reached a certain age and made the requisite number of mistakes.) But if it's a movie about what lessons we learn with age, it's also a movie about what lessons we fail to learn with age. And only when we get the privileged view of seeing the whole path of our life from the outside do we really know what to do. It's also a movie about what you're willing to kill for, and more importantly die for. These are the points where the movie is the strongest. In between are the action scenes, which are effective but border on being gratuitously bloody. I think that's just the style of the time, and you shouldn't expect anything less.
Running Time: 118 minutes
My Total Minutes: 298,733