Landau started acting in small roles in films and television shows such as "The Goldbergs" (1953) and "Armstrong Circle Theatre" (1956). His first major role was in the Alfred Hitchcock movie "North by Northwest" (1959) with Cary Grant. In 1966 he got the role of master of disguise Rollin Hand in the TV series "Mission Impossible", along with his wife, Barbara Bain. He played that role for three years and earned a Golden Globe Award in 1968. 