Makepeace made his film debut as one of the campers in Meatballs (1979) but first gained critical notice as the lead in My Bodyguard (1980). He went on to play Sean Penn's son in The Falcon and the Snowman and starred in Vamp, the TV movie The Undergrads (opposite Art Carney), and Captive Hearts (with Pat Morita), among others. His career slowed down after the 1990s and he later moved into the production end, including direction of commercials.