Roswell Hopkins Rudd Jr. was born November 17, 1935, in Sharon, Connecticut. He attended the Hotchkiss School before enrolling at Yale University, where in the mid-1950s he joined Eli's Chosen Six, a boisterous college dixieland band that recorded two albums, one of them for Columbia Records. It was an unlikely launching pad for a career that would eventually push the trombone into some of jazz's most radical territory, but Rudd himself always traced a direct line between the two: the collective, blues-and-rags interplay of trad jazz, learned playing for college crowds in Connecticut, taught him the horn-to-horn conversational language he would later bring into free improvisation.

After moving to New York, Rudd fell in with the city's emerging avant-garde. Around 1960-61 he played trombone on a session led by pianist Cecil Taylor and bassist Buell Neidlinger for Candid Records; a version of that date later circulated under the title New York City R&B (his contribution was one track, "Cell Walk for Celeste," alongside saxophonists Steve Lacy and Archie Shepp and drummers Denis Charles and Billy Higgins). Around the same time, Rudd and soprano saxophonist Steve Lacy — whose own career is covered in full in his JazzProfiles.com profile — formed a quartet, with bassist Henry Grimes and drummer Denis Charles, devoted entirely to the compositions of Thelonious Monk. Running from roughly 1961 to 1964, the Lacy-Rudd Quartet was one of the earliest examples of what would later be called jazz repertory: a working band built not around originals but around a single, still-living composer's book, with the horns filling in the harmonic space a piano would normally occupy. The only surviving recording of that group, a March 1963 set taped live at Manhattan's Phase Two Coffee House, wasn't released until 1975, on the British label Emanem, under the title School Days.

Rudd's other defining apprenticeship of the period was with Cecil Taylor — profiled separately at his JazzProfiles.com page — and with Archie Shepp, whom he began recording with around 1962; their most enduring collaboration, Shepp's 1964 Impulse! session Four for Trane, paired Rudd with John Tchicai, Reggie Workman, and Charles Moffett on an album of John Coltrane compositions produced by Coltrane himself. That Tchicai connection led directly to Rudd's most consequential 1960s project: in 1964 he co-founded the New York Art Quartet with Tchicai on alto saxophone, Milford Graves on drums, and Lewis Worrell on bass. The quartet's self-titled 1965 debut for ESP-Disk', which included a recitation by poet Amiri Baraka, became a foundational document of the free jazz movement's most uncompromising wing. Rudd made his own leader debut the following year with Everywhere (Impulse!, 1966), a quintet session with Robin Kenyatta, Giuseppi Logan, Worrell, and drummer Beaver Harris.

Through the late 1960s and 1970s Rudd moved fluidly across the era's most important large-ensemble projects: he appeared on Charlie Haden's Liberation Music Orchestra (1969) and Carla Bley's sprawling Escalator Over the Hill (1971), composed for the Jazz Composer's Orchestra, and released a run of leader albums — a self-titled 1971 date recorded in Europe with Tchicai, Flexible Flyer (1975), and Inside Job (1976). He and Lacy periodically reconvened, on Trickles (1976, Black Saint) and the quintet date Blown Bone (1979), and again in 1983 for Regeneration, a tribute to Monk and Herbie Nichols recorded with pianist Misha Mengelberg and drummer Han Bennink.

Starting in the 1960s and continuing on and off for roughly three decades, Rudd also worked alongside folklorist Alan Lomax, hand-coding the singing styles of the world's musical traditions for Lomax's Cantometrics project and, later, contributing to the Urban Strain study and the early Global Jukebox database — work that fed directly into the ethnomusicology courses Rudd went on to teach at Bard College and the University of Maine.

Rudd's recording career quieted through much of the 1980s and 1990s, though he resurfaced for projects with composer Allen Lowe and trombonist Steve Swell. He and Lacy reunited once more in 1999 for Monk's Dream (Verve), recorded in Paris with Lacy's regular rhythm section and singer Irene Aebi; the album drew a pair of Grammy nominations. The 2000s brought Rudd's most adventurous late-career turn, into world music proper: MALIcool (2002, Sunnyside), recorded with kora virtuoso Toumani Diabaté and a group of Malian musicians; Blue Mongol (2005), with Mongolia's Buryat Band; and El Espíritu Jíbaro (2007), a collaboration with Puerto Rican cuatro player Yomo Toro. The Jazz Journalists Association named him Trombonist of the Year five times across the decade (2003, 2004, 2005, 2009, and 2010).

Rudd kept recording into his final years — Trombone Tribe (2009), a nine-trombone summit; The Incredible Honk (2011); the Kickstarter-funded Trombone For Lovers (2013); duo and trio work with singer Heather Masse and organist John Medeski; and Strength & Power (2016) and Embrace (2017) with younger downtown improvisers. In 2013, Triple Point Records released Call It Art, a limited five-LP box documenting the New York Art Quartet's 1964-65 recordings in full. Rudd died December 21, 2017, at his home in Kerhonkson, New York, of prostate cancer, at age 82.

Rudd's career reads as one long argument that jazz's oldest and newest vocabularies were never as far apart as they looked. His trombone attack — broad, vocal, unapologetically brass-band in its roots — came straight out of the Dixieland and trad-jazz world of Eli's Chosen Six, and he never sanded it down; instead he carried it wholesale into some of the most abrasive free jazz of the 1960s, playing alongside Cecil Taylor and in his own New York Art Quartet with a tone that could suggest a New Orleans parade even inside total harmonic freedom. His work with Steve Lacy on the Monk songbook made him one of the form's first repertory specialists, prioritizing a single composer's architecture over either bebop convention or pure improvisation. That same appetite for structure carried him, decades later, into ethnomusicology and world music, where his trombone adapted itself to Malian griot traditions, Mongolian throat-singing ensembles, and Puerto Rican cuatro music with the same conversational, blues-rooted phrasing he'd developed playing rags in college.