Influenced by Charlie Chaplin and the escapism of the cinema, he pursued an acting career and attended the Actors Studio. In 1957, Landau made his Broadway debut in Middle of the Night. In 1959, Landau made his first major film appearance in Alfred Hitchcock's North by Northwest.
From 1966 to 1969, Landau played master of disguise Rollin Hand on the television show Mission: Impossible, for which he received multiple Emmy Award nominations. In 1988, he received a Golden Globe Award for Best Supporting Actor in a Motion Picture and Academy Award nomination for Best Supporting Actor for his work in Tucker: The Man and His Dream. He was nominated again for an Academy Award for Best Supporting Actor in 1989 for his role in Crimes and Misdemeanors. In 1994, he won the Academy Award for Best Supporting Actor for is supporting role of Bela Lugosi in Ed Wood, in addition to a Screen Actors Guild Award and a Golden Globe.
Landau married Barbara Bain on January 31, 1957. They divorced in 1993 and have two daughters, Susan and Juliet.
Landau lived his last years in West Hollywood, California, where he continued to perform in film and television and teach acting lessons. Landau received a star on the Hollywood Walk of Fame in recognition of his service to the entertainment industry, and was head of the Hollywood branch of the Actors Studio for many years. He died at the Ronald Reagan UCLA Medical Center in Los Angeles, California, on July 15, 2017, at age 89.