Slatkin was born in Los Angeles, California into a musical family - his father was the violinist, conductor and founder of the Hollywood String Quartet, Felix Slatkin, and his mother was the cellist with that quartet, Eleanor Aller.
He studied at Indiana University and Los Angeles City College before attending the Juilliard School where he studied conducting under Jean Paul Morel. His conducting debut came in 1966, and in 1968 he was made an assistant at the Saint Louis Symphony Orchestra. He stayed there until 1977, when he was made conductor of the New Orleans Philharmonic Orchestra, returning to St Louis in 1979 as music director. He remained there until 1996 when he took over the National Symphony Orchestra in Washington, D.C. In 2000 he was appointed principal conductor of the BBC Symphony Orchestra.
Slatkin has conducted a wide range of repertoire, being particularly noted for his interpretations of 20th century American music, and works by British composers. His compositions, which include The Raven for narrator and orchestra (after the poem by Edgar Allan Poe, 1971), are little known.