In movies, he was first cast in a number of bit parts, including a role as a sailor in the movie "Follow the Fleet" (1936), starring Fred Astaire and Ginger Rogers. He eventually signed with 20th Century-Fox and then Metro-Goldwyn-Mayer in which he starred in a number of musicals. Between 1938 and 1942, he made a number of hit records for Decca Records. Martin was featured in the 1941 Marx Brothers film "The Big Store", in which he played a singer and performed the now infamous (at least with Marx Brothers fans) "Tenement Symphony", which was written by Hal Borne, who became his long-time musical director.