Major Bill Cage is an officer who has never seen a day of combat when he is unceremoniously demoted and dropped into combat. Cage is killed within minutes, managing to take an alpha alien down with him. He awakens back at the beginning of the same day and is forced to fight and die again... and again - as physical contact with the alien has thrown him into a time loop. (TMDB)

In the year 2044, time travel has not yet been invented but in 30 years it will have been. When the mob wants to get rid of someone, they will send their target into the past where a looper, a hired gun, like Joe is waiting to mop up. Joe is getting rich and life is good until the day the mob decides to close the loop, sending back Joe's future self for assassination.