Landau died Saturday of "unexpected complications" after a brief stay at Ronald Reagan UCLA Medical Center, his representative confirmed to The Hollywood Reporter.
The veteran actor rose to prominence after playing a homosexual henchman in Alfred Hitchcock's 1959 film "North by Northwest".
He had more success in television, where he appeared in numerous guest roles on popular shows such as "Gunsmoke", "The Twilight Zone" and "The Alfred Hitchcock Hour". But it was the 1966 TV show "Mission: Impossible", which helped him make a mark in the industry. The actor portrayed an undercover disguise artist, Rollin Hand, on the show.
Landau then starred in Francis Ford Coppola's "Tucker: The Man and His Dream", where he played Abe Karatz, the business partner of visionary automaker Preston Tucker (Jeff Bridges). He even received the best supporting actor nomination for his performance.
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He received another best supporting actor Oscar nomination for Woody Allen's 1989 morality fable "Crimes and Misdemeanors", in which he played murderous opthamologist Judah Rosenthal. Landau finally won the golden statuette five years later for "Ed Wood".
"Ed Wood" featured Johnny Depp as legendary filmmaker Ed Wood. The film revolves around Wood's life when he made his best-known films as well as his relationship with actor Bela Lugosi.
The late star also was an admired acting teacher who taught the craft to the likes of Jack Nicholson.
Landau was last seen in Howard L Weiner's comedy drama "The Last Poker Game". The film debuted at the 2017 Tribeca Film Festival.
He is survived by his daughters Susie and Juliet from his marriage to Bain, sister Elinor, granddaughter Aria and godson Dylan.