In Atlanta, Georgia, a red car pulls up across the street from a bank. Inside are three robbers, Buddy (Jon Hamm), Darling (Eiza Gonzalez), and Griff (Jon Bernthal) and their getaway driver, Baby (Ansel Elgort). The robbers enter the bank while Baby jams out to the song "Bellbottoms". Moments later, the robbers run back to the car. Baby drives out of there with the music blaring in his ears. The police pursue the car throughout the city, but Baby is able to swiftly maneuver through obstacles to evade the cops. He drives on the highway where two other red cars are passing. Once they go under the bridge, Baby is able to trick the police and escape, taking the car to a parking garage where he and the robbers take another car and get away.
Later on, Baby goes to get coffee for himself and the crooks. They are meeting with their employer, Doc (Kevin Spacey). Griff asks why Baby is constantly listening to music. Doc says it's from an accident he had as a kid that left him with tinnitus, so he uses the music to drown out the humming. Griff messes with Baby to intimidate him, but Baby never flinches. The crooks part ways, and Buddy tells Baby to not answer Doc if he calls him again. Doc tells Baby to ignore that.
Baby lives with a paraplegic deaf man named Joseph (C.J. Jones). He keeps his share of the stolen money hidden under a floorboard. As he and Joseph communicate in sign language, Joseph knows Baby is in some kind of shady business. In his spare time, Baby takes recordings from his meetings with Doc and remixes them into music tapes. He keeps one special tape labeled "Mom".
Baby goes to Bo's Diner. He sees a pretty young waitress, Debora (Lily James), singing a song. She goes over to take his order, and she notices Baby's recorder. The two chat, and Baby asks what song Deborah is singing. He later finds the song and listens to it at home, leading Joseph to figure out that Baby has met a girl.
Doc brings Baby in for the next job. He introduces Baby to the new crew: Eddie No-Nose (Flea), JD (Lanny Joon), and Bats (Jamie Foxx). Their target is an armored truck. As Doc explains the plan, Baby listens to music. Bats is the first to question Baby's capabilities, but Baby is able to restate Doc's plan word-for-word. For Baby and Doc, this is the last job that Baby needs to take to settle a debt between him and Doc.
The crew gathers near the armored truck. JD already messes things up when he gets the wrong masks; Doc specified Michael Myers (of the "Halloween" movies) masks, but he gets "Austin Powers" Mike Myers masks. Baby waits in the car with his tunes while the three go rob the truck. Bats ends up killing the guard, and the three robbers frantically run back to the car. Baby tries to get out but hits the truck of a marine (Clay Donahue Fontenot). The marine shoots at the crooks, forcing Baby to drive against a wall to get out. The marine chases after them on the highway and causes them to get stuck under a truck. Bats gets a clear shot at the marine, but Baby pulls out to avoid this. The crooks then abandon their car and steal a car from a woman with a baby. JD ends up dropping his shotgun in the chaos. Baby drives off the highway and loses the marine when he crashes his truck. The gang makes it to the parking garage and moves to separate cars. Bats asks Baby if he purposely made him miss the shot. Baby says "no" but Bats knows he's lying. He holds a gun to Baby's face and threatens him for catching feelings.
Baby returns to Bo's Diner to continue seeing Debora. They chat about songs with their names, specifically how there are songs called "Debora" and "Debra", while there are lots of songs about "Baby".
Baby goes to Doc's hideout to get his cut of the money from the job. Only Bats and Eddie are there as well. Doc then has Baby dispose of the car that has JD's corpse in it. Baby takes the car to the junkyard and has a flashback about his childhood. He was very close with his mother (Sky Ferreira), who was a singer. His father was an alcoholic who abused her, and they got into a fatal car accident while arguing.
Baby takes on a new job as a pizza delivery driver. He is able to start seeing Debora socially. However, Baby is approached by Doc, who still needs him as a driver for more robbery jobs. Doc threatens Baby with potentially hurting Debora. Baby reluctantly agrees. He later takes Debora home and they have their first kiss.
Doc brings Baby to the post office where he wants to set the next heist. He has Baby go in with his nephew Sam (Brogan Hall) to provide a cover so Baby won't look suspicious being there alone. Sam scopes out the place to give Baby information to repeat back to Doc. They interact with a friendly teller (Allison King) before returning to Doc's car so Baby can give details for Doc to plan out the heist.
Baby calls Debora with a plan to drive far away and not look back. She agrees to it. Baby then has a black-and-white fantasy of Debora standing by a car, waiting for him to join her.
Despite his personal code of not using the same crew for more than one heist, Doc gathers Buddy, Darling, and Bats as his crew with Baby still being the getaway driver. Doc orders the crew to acquire guns from an arms dealer known as The Butcher (Paul Williams). On the ride to meet The Butcher, Baby pulls over at a convenience store so Bats can run inside. Buddy and Darling (who are married) get kinky in the backseat. Darling mentions that Bats looked at her funny, which irks Buddy, and he asks if she wants him to kill Bats, but Darling says not before the heist. Bats then comes back with a whole box of stolen gum.
The crew arrives at a warehouse to meet The Butcher and his thugs. The Butcher shows the crew his wide array of guns and rifles, and even some hand grenades. Bats notices the letters APD on the side of one of the gun boxes, leading him to realize The Butcher and his men are cops. Bats shoots The Butcher, forcing everyone into a shootout. The crew kills the majority of The Butcher's guys, but Darling gets shot in the arm. One guy nearly gets away, but the robbers shoot him, and Bats throws a grenade into his car for good measure. Buddy and Darling chastise Bats for starting the shootout, but he tells them that they were cops.
On the ride back to Doc's, Bats orders Baby to stop at Bo's Diner. Baby refuses for fear that they will hurt Debora, but Bats forces Baby to go there. Debora sees them but notices that Baby looks worried. She takes their order without letting the others know that she knows Baby, and vice versa. Buddy and Darling continue to get on Bats for what he did. As they get ready to leave, Bats asks Baby if he knows Debora. He says no. Bats gets up and pulls out his gun, but Baby grabs his hand before he does anything stupid. The crew leaves, and Baby hands Debora the check, her tip, and a not that says "Road Trip 2AM".
The crew returns to Doc. He knows something went wrong. Bats tells him that The Butcher and his guys were cops, but Doc already knew that because they were on his payroll. Bats lies and says they shot first, which Buddy and Darling back up. When Doc asks if the heist should or should not happen, he turns to Baby, who reluctantly insists that the heist go as planned.
Baby tries to sneak out at 2:00 AM to meet with Deborah, but he is followed by Buddy and Bats. When they get suspicious, Bats pulls out Baby's recorder and knocks him out.
Baby wakes up at Doc's table as Bats and Buddy take out all of Baby's tapes from his apartment. Bats is riding Joseph's wheelchair, though he insists he didn't hurt Joseph. Doc questions Baby about the tapes, but he proves they are just music tapes when he plays the one he recorded earlier after the first heist. Meanwhile, Deborah is left waiting for Baby.
The next morning, the crew heads to the post office to set the heist in motion. Buddy is supposed to take Darling hostage while Bats sneaks around the back. As Baby waits in the car, he sees the teller he met the previous day. She smiles and waves at him, but Baby shakes her head at her as if to warn her. The teller returns moments later with a guard. He taps on Baby's window just as the robbers return. Bats kills the guard, and the cops are on their way. The robbers press Baby to drive as he is hesitant. Bats aims his shotgun in Baby's face, so Baby hits the gas and drives forward into a truck with a steel bar sticking out, effectively impaling Bats. Baby, Buddy, and Darling all run for it.
The cops chase Baby through the city, even as he tries to change his appearance and steal different cars. He takes the car of an old lady (Andrea Frye), but he gives her back her purse. Baby runs into Buddy and Darling again as the cops close in on them. The couple attempts to escape with Baby, but the cops have them surrounded. Darling shoots at the cops, and the cops return fire, killing her. Buddy becomes enraged and fires at the cops while Baby gets away.
Baby returns to his apartment to find Joseph on the floor, but he is okay. He grabs whatever money he can and brings Joseph to a nursing home. Baby apologizes to Joseph for failing him when he said he wouldn't let anything happen to him. Baby runs as the police are still searching for him.
Baby runs to Bo's for Debora, only to find Buddy sitting at the counter with his gun. He wants Baby to pay for getting Darling killed, and he threatens Debora. A cop enters the diner, but he needs to use the restroom. Debora's co-worker comes out to ask how everything is, and when Buddy is distracted, Baby shoots him in the chest and runs away with Debora. They steal a car from two guys vaping and they head to Doc's. The cop then goes to check on Buddy, but Buddy shoots him dead.
When Baby and Debora meet with Doc, he is preparing to cut his losses with Baby, but Baby pleads for Doc's help and tries giving him the money from the heist. Doc relents and lets Baby take the money so that he and Debora can get away. They head down the elevator and find some of The Butcher's guys with guns. Doc gets shot twice but he manages to kill all three men. Buddy then arrives in a stolen cop car. He runs Doc over twice as he tries to go after Baby and Debora. Baby tries shooting at Buddy before trying to get him with another car. Baby rams Buddy's car over the edge of the railing, sending it falling several floors down. However, Buddy got out in time, and he shoots around Baby's ears to deafen him. He goes for Debora, who has taken a crowbar and tries to get Buddy. Baby gathers himself and grabs his gun, shooting Buddy in the leg and causing him to fall over onto the burning car, which then explodes.
In the morning, Debora is driving Baby far away while listening to the tape of Baby's mom singing. They then see that the police have formed a blockade, knowing they've caught Baby. Debora tries to get away, but Baby chooses to surrender.
Baby goes on trial for his part in the heists. Testimonies are given from Debora, Joseph, the post office teller, and the lady whose car Baby stole. All of them regard Baby as a good kid who made some bad choices and never meant to hurt anyone. The judge sentences Baby to 25 years in prison, with the possibility of parole in five years.
During his time in jail, Baby receives postcards from Debora, who has found out that Baby's real name is Miles. The cards are from places that they plan to see when Baby gets out.
We then see what looks like Baby's fantasy from earlier with Debora waiting for him. The scene shifts from black-and-white to color, indicating it is now five years later and Baby is out of prison. He goes to Debora and kisses her.