A member of the Tadd Dameron Sextet, in his heyday he was in demand for his ability to play at the rapid tempos typical of bebop, and appears on several key recordings of the period. He left the music business in the late 1950s.
On May 1, 1951 Russell played in the recording session for Un Poco Loco, composed by American jazz pianist Bud Powell, with Max Roach on drums. Literary critic Harold Bloom included this performance on his short list of the greatest works of twentieth-century American art.
According to jazz historian Phil Schaap, the classic bebop tune "Donna Lee", a contrafact on "Back Home Again In Indiana", was named after Curley's daughter. In 2002, she donated her father's bass to the Institute of Jazz Studies at Rutgers University.
- Charlie Parker: The Charlie Parker Story (Savoy Records, 1945)
- Charlie Parker: Memorial Vol. 1 (Savoy, 1947); Memorial Vol. 2 (Savoy 1947–48)
- Sonny Stitt: Sonny Stitt/Bud Powell/J. J. Johnson (Prestige, 1949–50 ) – with Bud Powell
- Charlie Parker: Bird and Diz, (Verve, 1950)
- Bud Powell: Jazz Giant (Verve, 1950)
- Fats Navarro: The Fabulous Fats Navarro (Blue Note Records, 1947–49)
- Miles Davis: The Real Birth of the Cool (Bandstand, 1948)
- Stan Getz: Early Stan (OJC, 1949–53)
- George Wallington: Trio (Savoy, 1949–51); Trios (OJC, 1952–53)
- Milt Jackson: Roll 'Em Bags (Savoy, 1949–56)
- Al Cohn: Cohn's Tones (OJC, 1950–53)
- Dexter Gordon: Dexter Rides Again (Savoy, 1950)
- Zoot Sims: Quartets (OJC, 1950)
- Bud Powell: The Amazing Bud Powell (Blue Note, 1951–53)
- Thelonious Monk: Thelonious Monk Trio/Blue Monk (Prestige Records, 1952–54); MONK (OJC, 1953–54)
- Al Cohn: Al Cohn's Tones (Savoy, 1953 )
- Kenny Drew: New Faces, New Sounds (Blue Note, 1953)
- Horace Silver: Horace Silver Trio (Blue Note, 1953)
- Art Blakey: A Night at Birdland Vol. 1 (Blue Note, 1954)
- Art Blakey: A Night at Birdland Vol. 2 (Blue Note, 1954)
- Art Blakey: A Night at Birdland Vol. 3 (Blue Note, 1954)
- Jay Jay Johnson: The Birdlanders (Fresh Sound, 1954)
- Thelonious Monk: Monk (Prestige, 1954)
- Johnny Griffin: Introducing Johnny Griffin (Blue Note, 1957)
- Cliff Jordan & John Gilmore: Blowing in from Chicago (Blue Note, 1957)
- Woideck, Carl Charlie Parker: his music and life University of Michigan Press, 1998 ISBN 0-472-08555-7, ISBN 978-0-472-08555-2 at Google Books
- Schaap learned this from saxophonist and music historian Allen Lowe, who was a friend of Russell's.
- "Donna Lee" @ jazzstandards.com. Accessed 2009-07-26
- The Curly Russell Bass: Restoration of a Musical Instrument Accessed 2014-12-24