Yes, this is two Joseph Gordon-Levitt movies in a row. (If you don't count The Hobbit, which was more of an Event.) Good catch.
I got to admit: I really kind of like that kid.
Hooray (by the way) for Netflix, who got this to the Pun Salad Manor mailbox on the exact day of the DVD release. I know they don't really like fogies like me getting old-fashioned physical media in the mail, but they (nonetheless) do a pretty good yob of it.
I'm going to describe the premise of this movie as it's laid out in the early going. It's set in the dystopian world of 2044, where vagrants wander the streets and criminals operate with impunity. But things are really bad in 2074. They have invented time travel by then, but it's illegal. The (even bolder) criminals of 2074 use it to send their victims back to 2044, where they are immediately blunderbussed by "loopers" and their bodies disposed of.
With me so far? OK: when a 2044 looper makes it to 2074, he is often time-machined back to 2044, where his younger self kills him. (Called "closing the loop.") If the 2044-looper fails to kill his older version, this is deemed to be "letting your loop run", and it's very unacceptable.
Now, all of that falls apart under very easy questioning. Why don't the 2074 bad guys just send their victims back to the Jurassic? Or to Antarctica, or the middle of the Pacific, or five miles above an active volcano? Cheaper, more reliable.
But once you swallow hard and buy the premise, this is actually a pretty good movie. Joseph Gordon-Levitt plays a young looper (Joe) confronted unexpectedly with his older self (Bruce Willis). Old Joe escapes Young Joe, and goes on the lam, looking for a young version of the criminal mastermind that's caused him some serious grief in 2074.
Good stuff! Joseph Gordon-Levitt underwent some serious makeup artistry to make him look more like a younger Bruce Willis. (Only problem being that we Moonlighting fans pretty much remember what the 30-years-younger Bruce Willis looked like, and he didn't look like that.)