According to The Hollywood Reporter, the actor "died Saturday of "unexpected complications" after a brief stay at UCLA Medical Center".
His publicist Dick Guttman confirmed the death, saying: 'We are overcome with sadness'.
Alfred Hitchcock saw the play and gave Landau his big break in movies, casting him in the 1959 classic North by Northwest. Landau finally earned an Oscar for playing horror-film legend Lugosi in the Tim Burton-directed biopic Ed Wood in 1994.
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Landau received an Emmy nomination for each of his three seasons on M:I, taking home the Golden Globe for Best TV Star - Male in 1968. Landau won the supporting actor Oscar. THR notes that Landau found a "kindred spirit" in Burton, who would later cast him in Sleepy Hollow and Frankenweenie.
Also in the 2000s, Landau worked as an acting coach in a venture with director Mark Rydell and screenwriter-playwriter Lyle Kessler. Landau would ultimately be instrumental in opening a West Coast branch of the Studio, and he'd continue teaching for the rest of his life.
Since then, Landau had worked steadily in film, including starring opposite Paul Sorvino in "The Last Poker Game", which premiered at the 2017 Tribeca Film Festival in NY.
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Landau starred in Cleopatra, The Greatest Story Ever Told and Nevada Smith, before joining the cast of TV's Mission:Impossible. On both shows, he co-starred with Barbara Bain, his wife from 1957 to 1993. "I would've probably died playing that role". Interestingly, Leonard Nimoy would got on to essentially replace Landau in M:I when the latter left in 1969.
Nearly two decades later, after some lean years, Landau enjoyed a career revival in feature films.
The man who would eventually star in Mission: Impossible and Ed Wood began his career as a cartoonist for the New York Daily News, but eventually segued into acting, attending the famed Actors Studio with James Dean and Steve McQueen.
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That 1995 Golden Globe Award, his second for best supporting actor in a movie, trailed one for his role as an emigre financier in the story about a maverick auto designer, "Tucker: The Man and His Dream" (1989). (He was also nominated three times for "Mission: Impossible", although he never won an Emmy.) In 2015 he appeared in the "Entourage" movie.