He and his identical twin brother, double bassist Addison Farmer, started playing professionally while at high school in Los Angeles.

He subsequently moved from Los Angeles to New York, where he performed and recorded with musicians such as Horace Silver, Sonny Rollins, and Gigi Gryce and became known principally as a bebop player.

As Farmer's reputation grew, he expanded from bebop into more experimental forms through working with composers such as George Russell and Teddy Charles.

[3] Farmer and his brother moved to Los Angeles in 1945, attending the music-oriented Jefferson High School, where they got music instruction and met other developing musicians such as Sonny Criss, Ernie Andrews, Big Jay McNeely, and Ed Thigpen.

Art started playing trumpet professionally at the age of 16,[8]: 261  performing in the bands of Horace Henderson, Jimmy Mundy, and Floyd Ray, among others.

[3]: 50  Farmer's trumpet influences in the 1940s were Dizzy Gillespie, Miles Davis and Fats Navarro, but, in his own words, "then I heard Freddie Webster, and I loved his sound.

[10][12] Performing for long periods seven days a week for this job put great pressure on his technique, which was insufficiently developed to cope with such physical demands.

[13] Farmer's first studio recording appears to have been on June 28 or July 2, 1948, in Los Angeles, under the leadership of vocalist Big Joe Turner and pianist Pete Johnson.

[16][17] Farmer worked in Los Angeles for a time as a hotel janitor and a hospital file clerk, before joining Lionel Hampton's orchestra in 1952.

He toured Europe with the orchestra from September to December 1953,[18] and shared the organization's trumpet chairs with Clifford Brown, Quincy Jones and Benny Bailey.

This was combined with another recorded 11 months later to form the eight-track Prestige LP, The Art Farmer Septet, featuring arrangements by Quincy Jones and Gigi Gryce.

[23]: 406  One of the others was pianist Thelonious Monk, who led a sextet that included Farmer on its performances on a version of the Steve Allen Show, broadcast on television on June 10, 1955.

[26][27] The transition from Silver's piano-led quintet to Mulligan's piano-less quartet was not straightforward: "to suddenly find yourself in a pianoless group was like walking down the street naked", commented Farmer.

[6]: 442 From the middle of the 1950s, Farmer featured in recordings by leading arrangers of the day, including George Russell, Quincy Jones and Oliver Nelson, being in demand because of his reputation for being able to play anything.

[3] The wide range of styles these arrangers represented was extended when Farmer took part in a series of experimental sessions with composer Edgard Varèse in 1957.

[34][35] Hall left the second tour while the quartet, which included Swallow and drummer Pete La Roca, was engaged in Berlin, and a pianist replaced him; this was ultimately Steve Kuhn.

[22]: 45  Work opportunities, however, were diminishing as rock became more popular in the mid-1960s, so Farmer joined the pit orchestra of Elliot Lawrence for the production of The Apple Tree on Broadway, for six months.

[19] Farmer moved there in 1968 and ultimately settled in Vienna, where he performed with The Kenny Clarke/Francy Boland Big Band[23]: 406  and joined the Austrian Radio Orchestra.

[5] The latter job initially required only ten days a month of his time, so he was able to play with other well-known expatriates such as Don Byas, Dexter Gordon, and Ben Webster.

He had regular gigs with Clifford Jordan at the Sweet Basil Jazz Club and, later, with Ran Blake and Jerome Richardson at the Village Vanguard, both in New York.

[3][17][42] They lived together in a house that they had built in Vienna, and Farmer reported contentment with his lifestyle; notably, in contrast with his homeland, he did not experience racism in Europe.

One comment on a concert given when Farmer was 67 was that "his style was continuing to evolve"; he "delivered several solos in which his characteristically flowing lines were interrupted by sudden, wide melodic leaps and disjunct rhythmic accents".

[5] A few months before his death, although faster numbers had become perhaps too challenging, The Guardian observed, Farmer's playing on slower tunes achieved a new level of emotional expression.