In 2074, when the mob wants to get rid of someone, the target is sent into the past, where a hired gun awaits - someone like Joe - who one day learns the mob wants to 'close the loop' by sending back Joe's future self for assassination.

Joe: Then I saw it. I saw a mom who would die for her son. A man who would kill for his wife. A boy, angry and alone. Laid out in front of him, the bad path. I saw it. And the path was a circle. Round and round. So I changed it.
Abe: [Joe has been teaching himself French] Why the fuck French?
Joe: I'm going to France.
Abe: You should go to China.
Joe: I'm going to France.
Abe: I'm from the future. You should go to China.
[first lines]
Joe: Time travel has not yet been invented. But thirty years from now, it will have been. It will be instantly outlawed, used only in secret by only the largest criminal organizations. It's nearly impossible to dispose of a body in the future... I'm told. Tagging techniques, whatnot. So when these criminal organizations in the future need someone gone, they use specialized assassins in our present called "Loopers." And so, my employers in the future nab the target, they zap them back to me - their Looper. He appears, hands tied and head sacked, and I do the necessaries. Collect my silver. So the target has vanished from the future, and I've just disposed of a body that technically does not exist. Clean.
Older Joe: I don't want to talk about time travel because if we start talking about it then we're going to be here all day talking about it, making diagrams with straws.
Joe: Then I saw it, I saw a mom who would die for her son, a man who would kill for his wife, a boy, angry & alone, laid out in front of him the bad path. I saw it & the path was a circle, round & round. So I changed it.
Abe: This time travel crap, just fries your brain like a egg...
Joe: There's a reason we're called loopers. When we sign up for this job, taking out the future's garbage, we also agree to a very specific proviso. Time travel in the future is so illegal, that when our employers want to close our contracts, they'll also want to erase any trace of their relationship with us ever existing. So if we're still alive 30 years from now, they'll find our older self, zap him back to us, and we'll kill him like any other job. This is called closing your loop.
Older Joe: How's your French coming?
Joe: Good. You gonna tell me I ought to be learning Mandarin?
Older Joe: I never regretted learning French.
[in French]
Older Joe: I know you have a gun between your legs.
[in English]
Older Joe: No? Well, you'll get it eventually. Obviously.
Joe: All right, listen. This is a hard situation for you, but we both know how this has to go down. I can't let you walk away from this diner alive. This is my life now. I earned it. You had yours already. So why don't you do what old man do and die? Get the fuck out of my way.
Older Joe: Why don't you just take out your little gun from between your legs and do it? Boy.
Older Joe: My memory's cloudy. It's a cloud. Because my memories aren't really memories. They're just one possible eventuality now. And they grow clearer or cloudier as they become more are less likely. But then they get to the present moment, and they're instantly clear again. I can remember what you do after you do it. And it hurts.
Joe: So even when we're apart, you can remember what I do after?
Older Joe: Yes, but this is a precise description of a fuzzy mechanism. It's messy.
Abe: My great-grandfather told my grandfather, "Men are like spiders. It's the little ones you've got to be careful of."
Joe: Don't know I agree with that.
Abe: Yeah? Huh. What the fuck did my great-grandfather know?
Older Joe: This is a piece of indentifying information on the Rainmaker. He's here. He lives here now. In this county. And I'm gonna use this to find him. And I'm gonna kill him. I'm gonna stop him from killing my wife.
Joe: Fuck you. And your wife. None of this concerns me.
Older Joe: This is gonna happen...
Joe: It happened to you. It doesn't have to happen to me. You got a picture right there in my watch? Let me see. Show me the picture. As soon as I see her, I walk away. I'll fucking marry someone else. Promise. So when I see that picture, that fog inside your brain should just swallow up all the memories, right? She'll be gone. If you give her up, she'll be safe.
Older Joe: Give her up?
Joe: Yeah, give her up. Your the one who got her killed. She never meets you, she's safe.
Older Joe: You don't understand. We don't have to give her up. I'm not gonna give her up. I'm gonna save her.
Sara: This is a Remington 870. One blast could cut you the fuck in half.
Joe: In half. Yeah, that's telling. You're holding a gun, I say I'm not afraid, so you describe the gun to me. It's not the gun I'm not afraid of.
Older Joe: You know, there's another girl who works here on the weekends.
Joe: Jen?
Older Joe: Right. Less letters.
Joe: That'd be better.
Joe: [to Old Joe] Your face looks backwards.
Cid: You're a liar, you're gonna get killed 'cuz you won't stop lying.
Kid Blue: [Waving his gun] Know why they call that peashooter of yours blunderbuss? Because it's impossible to hit anything farther than 15 yards. Impossible to miss anything closer. It's a gun for fuck-up turkeys.
Joe: Kid, cut it out. Don't blow your other foot off.
Sara: [points her gun at the sugar cane field] Listen up, fucker! I have shot and buried three vagrants in the past year! So I don't care what hobo sob story you've got. I get a dozen a week, pal. It cuts no cash for me. But if you show your face here again, I will cut you the fuck in half!
[from trailer]
Joe: Loopers are well paid, they lead a good life...
[from trailer]
Older Joe: I'm going to stop this guy.
Joe: None of this concerns me...
Older Joe: It is going to happen to you!
Joe: It's going to happen to YOU, it's not going to happen to ME!
Joe: Time travel hasn't been invented yet, but in thirty years, it will have been. It's gonna be used by these three criminal syndicates.
Sara: You're a looper?
Abe: Ask yourself: who would I sacrifice for what's MINE?
[last lines]
Cid: Where's Joe?
Sara: He had to go away, baby.
[from trailer]
Joe: I work as a specialized assassin, in an outfit called the Loopers. When my organization from the future wants someone to die, they zap them back to me and I eliminate the target from the future. The only rule is: never let your target escape... even if your target is you.
[from trailer]
Older Joe: [to his younger self] He's gonna take everything YOU got, and everything I got!
Abe: I guess everything comes back around. Like your goddamn ties.
[from trailer]
Joe: [to his clients] I'm gonna fix this! I'm gonna find him, and I'm gonna kill him!
[from trailer]
Sara: You're going to kill this guy, your own self?