Hunted by your future. Haunted by your past.
Why it is hard sci-fi
Time travel in 2074 is illegal and used by organised crime to dispose of bodies. A looper kills a target sent back from the future, and one day the target is the looper himself. The film commits to a single mutable timeline. Younger Joe carries scars given to Older Joe in real time. The economy of contracts and the political legitimacy of the looper job are part of the worldbuilding.
Science inside it
A working time-travel rule that produces visible feedback. Younger and older versions of the same person can occupy the same room, and a change to the younger version propagates onto the older version with a delay that the film uses for staging. The rules are not consistent under hard scrutiny but the film admits as much in a famous line about not getting into the time-travel logic.
Spoiler alert
Younger Joe shoots himself to break the loop and stop Older Joe from killing the boy who would grow up to be the Rainmaker. The film is honest that a single suicide loop is the cleanest solution and presents it as a deliberate ethical choice rather than a stunt.