Winner of four Grammy Awards and recipient of the Jazz Master title from the National Endowment of the Arts. He is a multi-instrumentalist, talented at playing alto saxophone and clarinety.
He studied at the Manhattan School of Music and at The Juilliard School before moving towards avant-garde jazz.
He co-founded the Delaware Water Gap Celebration of the Arts, a group that was established to help foster the appreciate of the arts.
He married Chan Parker, Charlie Parker's widow.
Woods played the saxophone solo on Paul Simon's song "Have a Good Time."