David Gompper has lived and worked professionally as a pianist, a conductor, and a composer in New York, San Diego, London, Nigeria, Michigan, Texas and Iowa. He studied at the Royal College of Music in London with Jeremy Dale Roberts and Humphrey Searle. After teaching in Nigeria, he received his doctorate at the University of Michigan and taught at the University of Texas, Arlington. Since 1991, he has been Professor of Composition and Director of the Center for New Music at the University of Iowa. In 2002-2003 Gompper was in Russia as a Fulbright Scholar, teaching, performing and conducting at the Moscow Conservatory. In 2009 he received an Academy Award from the American Academy of Arts and Letters in New York City, a Fromm Commission in 2013, and a Guggenheim in 2020.

Gompper's compositions have been performed at Carnegie Hall, Lincoln Center and Merkin Halls (New York), Wigmore Hall (London), Konzerthaus (Vienna) and the Bolshoi and Rachmaninoff Halls (Moscow Conservatory). His compositions have been released on 17 discs, including his Violin Concerto with Wolfgang David and the Royal Philharmonic Orchestra on the Naxos label. As a pianist, he continues to maintain an active profile accompanying musicians and singers, including Wolfgang David (violin), Stephen Swanson & John Muriello (baritones), Michael Norsworthy (clarinet), Christine Rutledge (viola), Timothy Gill (cello) and Volkan Orhon (double bass).