A saxophonist, flautist and pianist. He was a member of the Mothers of Invention and later worked with Frank Zappa on his solo recordings, most notably on 1969's Hot Rats.

He married Ruth Komanoff (Underwood), marimbist/percussionist for the Mothers of Invention (mainly 1970s).

After his lengthy career with Zappa, he pursued a career as a session keyboardist and is known for his proficiency on the Minimoog synthesizer. His work includes various projects, including recordings for Quincy Jones, Barbra Streisand, Hugh Cornwell and Barry Manilow.

Underwood has also been a featured performer (mostly on piano) with James Horner on several of Horner's film scores, notably Titanic (1997) and Sneakers (1992).