The New Yorker's work became synonymous with the New Hollywood of the 1970s.
His coming-of-age drama, 1971's The Last Picture Show, which he also co-wrote, earned him eight Oscar nominations including best director.
The film, set in a Texas town, had an ensemble cast of rising stars including Jeff Bridges and Cybill Shepherd.
In 2014, he returned with his first movie in 13 years. She's Funny that Way, starring Owen Wilson and Imogen Poots, was "a celebration of old Hollywood", wrote BBC Culture's Nicholas Barber at the time.
Bogdanovich also starred on the small screen, appearing on HBO's The Sopranos where he played the role of a psychotherapist.
Born in 1939, Bogdanovich became interested in cinema from an early age.
Between the ages of 12 and 30, he kept a record of every film he watched along with a small review on an index card.
As a teenager, he attended acting school and upon leaving took up small roles in theatre and on television, the New York Times reports.
Bogdanovich is survived by his two children.
Francis Ford Coppola, director of The Godfather, released a statement to Deadline to say he was "devastated" by the news.
"May he sleep in bliss for eternity, enjoying the thrill of our applause forever", he said.
Guillermo del Toro, the director of Pan's Labyrinth, tweeted: "He was a dear friend and a champion of Cinema... He single-handedly interviewed and enshrined the lives and work of more classic filmmakers than almost anyone else in his generation."