Just like Inception, this is a movie where you have to pay attention. There are at least two concurrent story-lines occurring. I made it more.
You will possibly want more than one viewing, so you follow one or the other. There will be details that are only caught when you know what you're looking for.
However, it doesn't feel that confusing when you're watching it. It's only afterwards that kicks in. It's when you realize that the two people sitting either side of you saw two different movies; and neither was the one that you saw.
The meat of the movie concerns what happens when the Mafia get time travel. One mobster returned in time to recruit assassins. It was easy to do, as society is more than a little rough in 2042 America.
Anyone who crosses the mob in 2072 is zapped back in time. They barely have a second to draw breath before, handcuffed and hooded, they are shot dead by the waiting hit-men. Their murderers are the Loopers.
But one day that man being killed will be yourself. It's called 'closing the loop' and it's understood.
What is also understood are the consequences to not pulling that trigger, even against your older self. I think I will be having nightmares for a while at the implications of what happened to one young Looper.
Joe knows this. That is why, when his older self fights back, he is so determined to hunt him down and 'close the loop'. But there are complications, not least that the older Joe has had thirty years more experience at this game, and an agenda of his own.
There's a sub-plot too, just to make life even more interesting. A tenth of the population has evolved telekinesis. By the second act of the movie, it's like flicking between The Godfather and Carrie.
But again, and I can't reiterate this enough - it works!