The story starts off with Gordon-Levitt narrating what 2044 will present to us. It will have Loopers, time travelers from 2074 as hired assassins to kill mafia targets of the 30 years ahead. To retire a looper, the future self is sent to 2044 and killed by their past self. This happens to Gordon-Levitt's Joe, and his older self (Bruce Willis) flees.
Old Joe explains of a mob boss called the Rainmaker, who's evil in 2074 has inspired Old Joe to warn young Joe when his loop is closing. Old Joe has a list of three young children who could potentially be the Rainmaker. It just so happens that reluctant young Joe meets the Rainmaker, and Old Joe is out potentially killing two innocent children.
