Originally self-taught, Burton attended Boston's Berklee College of Music, where he subsequently returned in 1971 as a teacher, eventually becoming a major figure in jazz education. He was also a child prodigy, with a major label contract by the time he became a student. One of the major innovators on the vibraphone, he adopted many aspects of keyboard technique, including playing simultaneously with four mallets, allowing him to play chords or melody lines (or a mixture of both).
In the early 1960s he worked with George Shearing, and then Stan Getz. He founded his own quartet in 1967, starting a long collaboration with bassist Steve Swallow. Guitarists in the group included, over time, Larry Coryell, Pat Metheny and John Scofield. From the outset, Burton played music that drew heavily on rock influences. His quartet (plus violinist Richard Greene) recorded music by Burton and Michael Gibbs on the pioneering jazz-rock album Throb (1969), and a larger line-up recorded Carla Bley's composition A Genuine Tong Funeral (1967).
Subsequent Burton line-ups have developed his vibes style, combined with a reputation for talent-spotting. Among the musicians who made some of their earliest recordings with his groups are Scottish saxophonist Tommy Smith, Japanese pianist Makoto Ozone and Austrian guitarist Wolfgang Muthspiel. Burton has also played in several duos, with Swallow, with guitarist Ralph Towner, and most successfully of all, with Chick Corea, with whom he has made several discs (including the famous Crystal Silence) and plays one or two concerts each year. Burton and Corea were also reuinted on Burton's 1997 all-star Grammy-winning disc Like Minds.