CNN and The Hollywood Reporter say he died at his home in Manhattan, New York, of natural causes.
Their most well-known film, "Grey Gardens" (1975), was a profile of Jacqueline Onassis' eccentric cousins -- mother and daughter Big Edie and Little Edie Bouvier -- who lived in a dilapidated, cat-packed estate in East Hampton, New York. The brothers worked with fellow directors Ellen Hovde and Muffie Meyer on the film, which was remade as a Tony-winning Broadway play and as an award-winning 2009 HBO drama that starred Drew Barrymore and Jessica Lange.
"The excitement in making a documentary film is that it's for real and you don't what's coming up next. It's more than one can imagine," Maysles said in the interview.
Maysles had a long relationship with Christo, making five films about the artist's work. From The New York Times:
The first was “Christo’s Valley Curtain” (1974), which was nominated for a documentary short-subject Oscar, and the last was “The Gates” (2005), about the artists’ temporary transformation of Central Park.
His brother, David Maysles, died in 1987.
Here's a clip from the first part of "Valley Curtain."