In February 1961, Llewyn Davis (Oscar Isaac) is a struggling folk singer (previously a merchant marine) in New York City's Greenwich Village. His musical partner, Mike, has committed suicide; Llewyn's recent solo album Inside Llewyn Davis is not selling; he has no money and is sleeping on the couches of friends and acquaintances.
Llewyn performs in the Gaslight Cafe ("Hang Me, Oh Hang Me"), and club owner Pappi (Max Casella) tells him someone is waiting for him. Outside, a shadowy man in a suit beats Llewyn for having heckled a performance at the venue the previous night.
Llewyn sleeps at the Upper West Side apartment of his older friends the Gorfeins. The next morning, he listens to one track from his and Mike's album "If We Had Wings" ("Dink's Song", not to be confused with another traditional ballad, "Fare Thee Well (Ten Thousand Miles)"). When Llewyn leaves the apartment, the Gorfeins' orange tabby cat (a male) gets locked out. Llewyn takes the cat to the West Village apartment of his friends Jim (Justin Timberlake) and Jean (Carey Mulligan). Llewyn visits his manager, who explains that Llewyn's album is not selling, but claims he sent a copy to Chicago producer Bud Grossman (a character based on impresario Albert Grossman).
Jean secretly tells Llewyn she is pregnant, and fearing that she was impregnated by Llewyn instead of Jim, asks him to pay for an abortion. The three friends attend the Gaslight Cafe. Llewyn unsuccessfully asks Jim for money. Jim, Jean, and their guest Troy Nelson (Stark Sands) perform "Five Hundred Miles". The next morning, it seems that the Gorfeins' cat escapes again.
Llewyn visits his sister in Woodside, Queens, hoping to borrow money, and tells her to throw out a box of his papers. On Jim's invitation, Llewyn, as part of the "John Glenn Singers", records a novelty song with Jim and Al Cody (Adam Driver), "Please Mr. Kennedy". Llewyn needs money immediately and agrees to $200, with no royalties.
At the gynecologist's office, Llewyn sets up Jean's appointment. The doctor says that two years previously, Llewyn had paid in advance for another woman who then decided to keep the baby and moved to Akron. Llewyn and Jean argue about his lack of direction. On the street Llewyn grabs what appears to be the Gorfeins' orange cat; that evening he takes the cat back, and is invited in to have dinner. He is rude the Gorfeins' guests and when asked to play after dinner reluctantly starts playing "Fare Thee Well". Mrs. Gorfein starts to sing the harmony -- which was Mike's part -- but Llewyn snaps, insulting the Gorfeins and their guests. Mrs. Gorfein leaves the table crying, coming back when she discovers that the orange cat is not theirs; Llewyn takes the cat and leaves.
Llewyn rides with two musicians driving to Chicago: the laconic Johnny Five (Garrett Hedlund), a beat poet, and the disagreeable Roland Turner (John Goodman), a jazz musician. Roland insults Llewyn: demeaning folk music, making fun of his name, and ridiculing a grown man traveling with a cat. Later Llewyn plays his guitar ("Green, Green Rocky Road"). At a roadside restaurant, Roland collapses from a heroin overdose in the bathroom. The three continue, eventually stopping on the side of the highway that night to rest. When a police officer tells them to move on, Johnny resists and is arrested. Left without the keys, Llewyn abandons the car, with the cat and the unconscious Roland inside.
In Chicago, Llewyn seeks out Bud Grossman (F. Murray Abraham), who says he never received a copy of Llewyn's record, but agrees to an audition. Llewyn plays "The Death of Queen Jane"; Grossman is not encouraging.
Llewyn hitchhikes back to New York and hits what may be yet another or perhaps the same orange cat with the car he is driving. He considers briefly detouring to see his son in Akron. Back in New York he pays $148 to rejoin the merchant marines. He also visits his ailing father, singing him "The Shoals of Herring". Llewyn then starts to say goodbye to Jean; she tells him that Pappi will let him play at the Gaslight again. Llewyn searches for his shipping license required to ship out but it was in the box his sister threw out. The union office can issue a new license, but at a price that Llewyn cannot now afford.
At the Gaslight, an Irish quartet performs "The Auld Triangle". Pappi states that he had sex with Jean, suggesting that he pressures female performers he finds attractive to do so in order to perform at the Gaslight. Llewyn becomes upset and loudly heckles an older woman playing "The Storms Are On the Ocean". He is thrown out and goes to the Gorfeins' apartment. They graciously welcome him; he is amazed to see that their orange cat Ulysses found his way home, arriving the previous day.
The next morning is nearly identical to his stay at the Gorfeins' at the beginning of the film, although this time he blocks the cat from escaping. On the street he gazes at a poster for The Incredible Journey, wondering about all his sightings of an orange cat.
He performs at the Gaslight, singing "Hang Me, Oh Hang Me" and finishing with a raw, emotional solo performance of "If I Had Wings". Pappi teases him about his heckling the previous evening and tells him that a friend is waiting outside. As Llewyn leaves the building, a young Bob Dylan takes the stage and begins to sing. Behind the Gaslight, Llewyn is confronted by a shadowy man in a suit, who beats him for rudely heckling the previous night's performance, who he reveals was his wife. Llewyn watches the man get in a taxi, commenting "Au revoir".