American jazz musician, one of the most distinctive and creative bop-era (bebop) tenor saxophonists, who in later years played soprano saxophone as well.

Thompson played tenor saxophone in the early 1940s with Lionel Hampton (Hampton, Lionel), the Billy Eckstine (Eckstine, Billy) band, and Count Basie (Basie, Count) before a highly active period in Los Angeles working with Dizzy Gillespie (Gillespie, Dizzy), Charlie Parker (Parker, Charlie), Charles Mingus (Mingus, Charles), Boyd Raeburn, and other pioneers of bebop. Even in this early stage of his career, Thompson revealed an original improvising approach. His beautiful tone was reminiscent of Ben Webster's, with a rough edge in climactic passages; much of his phrasing was influenced by the early works of Don Byas (Byas, Don), and his solo style was a more modern development of the Webster saxophone tradition. A subtle sense of expression, of unusual, accented harmonies, and of dramatic solo form characterized his finest work, specifically in his 1950s recordings as a bandleader (including his unique saxophone-guitar-bass trio in Tricotism 【1956】) and with Milt Jackson (Jackson, Milt), Jo Jones (Jones, Jo), and Miles Davis (Davis, Miles).

Thompson lived in Europe for extended periods in the 1950s and '60s. He was less active upon subsequent returns to the United States, during which he emphasized the lyrical qualities of his style and soloed increasingly on soprano saxophone. He taught at Dartmouth College (1973–74), but disenchantment with the music business led to his early retirement.