In a brief scene in 1964, an aging, overweight Italian American, Jake LaMotta (Robert De Niro), practices a comedy routine. The rest of the film then occurs in flashback. In 1941, LaMotta is in a major boxing match against Jimmy Reeves, where he received his first loss. Jake's brother Joey LaMotta (Joe Pesci) discusses a potential shot for the middleweight title with one of his Mafia connections, Salvy Batts (Frank Vincent). Some time thereafter, Jake spots a 15-year-old girl named Vikki (Cathy Moriarty) at an open-air swimming pool in his Bronx neighborhood. He eventually pursues a relationship with her, even though he is already married. In 1943, Jake defeats Sugar Ray Robinson, and has a rematch three weeks later. Despite the fact that Jake dominates Robinson during the bout, the judges surprisingly rule in favor of Robinson and Joey feels Robinson won only because he was enlisting into the US Army the following week. By 1947, Jake marries Vikki.
Jake constantly worries about Vikki having feelings for other men, particularly when she makes an off-hand comment about Tony Janiro, Jake's opponent in his next fight. His jealousy is evident when he brutally defeats Janiro in front of the local Mob boss, Tommy Como (Nicholas Colasanto), and Vikki. As Joey discusses the victory with journalists at the Copacabana, he is distracted by seeing Vikki approach a table with Salvy and his crew. Joey speaks with Vikki, who says she is giving up on his brother. Blaming Salvy, Joey viciously attacks him in a fight that spills outside of the club. Como later orders them to apologize, and has Joey tell Jake that if he wants a chance at the championship title, which Como controls, he will have to take a dive first. In a match against Billy Fox, after briefly pummeling his opponent, Jake does not even bother to put up a fight. He is suspended shortly thereafter from the board on suspicion of throwing the fight, though he realizes the error of his judgment when it is too late. He is eventually reinstated, and in 1949, wins the middleweight championship title against Marcel Cerdan.
A year later, Jake asks Joey if he fought with Salvy at the Copacabana because of Vikki. Jake then asks if Joey had an affair with her; Joey refuses to answer, insults Jake, and leaves. Jake directly asks Vikki about the affair, and when she hides from him in the bathroom, he breaks down the door, prompting her to sarcastically state that she had sex with the entire neighborhood (including his brother, Salvy, and Tommy Como). Jake angrily walks to Joey's house, with Vikki following him, and assaults Joey in front of his wife and children. After defending his championship belt in a grueling fifteen round bout against Laurent Dauthuille in 1950, he makes a call to his brother after the fight, but when Joey assumes Salvy is on the other end and starts insulting and cursing at him, Jake says nothing and hangs up. Estranged from Joey, Jake's career begins to decline slowly and he eventually loses his title to Sugar Ray Robinson in their final encounter in 1951.
By 1956, Jake and his family have moved to Miami. After he stays out all night at his new nightclub there, Vikki tells him she wants a divorce (which she has been planning since his retirement) as well as full custody of their kids. She also threatens to call the cops if he comes anywhere near them. He is later arrested for introducing under-age girls to men in his club. He tries and fails to bribe his way out of his criminal case using the jewels from his championship belt instead of selling the belt itself. In 1957 he goes to jail where he pounds the walls, sorrowfully questioning his misfortune and crying in despair. Upon returning to New York City in 1958, he happens upon his estranged brother Joey, who forgives him but is elusive. Returning to the opening scene in 1964, Jake refers to the "I coulda been a contender" scene from the 1954 film On the Waterfront starring Marlon Brando, complaining that his brother should have been there for him but is also keen enough to give himself some slack. After a stagehand [played by director Martin Scorsese in a brief cameo] informs him that the auditorium where he is about to perform is crowded, Jake starts to chant "I'm the boss" while shadowboxing.
The film cuts to black with the following Biblical quote filling the screen:
So, for the second time, [the Pharisees] summoned the man who had been blind and said:

"Speak the truth before God. We know this fellow is a sinner."

"Whether or not he is a sinner, I do not know," the man replied.

"All I know is this: Once I was blind and now I can see."
John IX. 24â26, The New English Bible
The film subsequently ends with an on-screen dedication to Scorsese's New York University film professor, Haig P. Manoogian:
Remembering Haig P. Manoogian, teacher. May 23, 1916 â May 26, 1980. With Love and resolution, Marty.

Question: Where do Jake and his family move in 1956?
Answer: Miami, Florida
Alternative answer: They move to Miami.