Bogdanovich, known for films such as The Last Picture Show and Mask, died of natural causes on Thursday morning at his home in Los Angeles, his daughter Antonia Bogdanovich said.
Speaking in a video posted to Instagram Baldwin described Bogdanovich as a “wonderful raconteur” and praised his 1973 comedy Paper Moon.
“I met him a couple of times and was a great admirer of his. He was a real iconoclast,” he said.
“Wonderful film maker, wonderful raconteur, interesting guy, wonderful writer and… he was definitely one of those larger than life figures in the entertainment and movie business.
Speaking about Bogdanovich’s films he added: “They’re very peaceful, they’re very funny but there’s a warmth and a great humanity to them.
“Rest in peace Peter Bogdanovich.”
The Big Lebowski star Jeff Bridges said Bogdanovich had left behind the gift of “his incredible films and insights”.
“My heart is broken – my dear friend Peter is no longer with us in the physical form,” the actor tweeted.
“I loved him and will miss him. What a wonderful artist.
“He’s left us with the gift of his incredible films and his insights on the filmmakers he so admired. I love you Peter.”
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Multi-award winning actress Dern said Bogdanovich “taught me so much” and gave her a first great acting opportunity.
Posting a photo to Instagram of the set of the 1985 film Mask, she wrote: “Another hero lost.
“My teacher and guide, who gave me my first great acting opportunity.
“My friend through life, who taught me so much about filmmaking.
“I love you, Peter, with everything.”
Legendary US singers Streisand and Cher, who both appeared in Bogdanovich’s films, expressed their sadness at the loss.
Streisand, who starred in his 1972 screwball comedy What’s Up, Doc?, said: “Peter always made me laugh!
“He’ll keep making them laugh up there too. May he rest in peace.”
Cher, who starred in Mask alongside Dern, said the director had discovered “amazingly talented artists” throughout his career.
Bogdanovich was born in Kingston, New York, in 1939, and started out as a film journalist and critic before moving on to film-making.
His well-known films include The Last Picture Show in 1971, which earned eight Oscar nominations, and Paper Moon in 1973.
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