The Lions For Lambs star founded the festival in 1985, as an offshoot of his Sundance Institute that offers professional support to indie filmmakers, showing less than 30 films. This year the festival, in Park City, Utah, is playing 119 feature films from 32 countries, culled from about 4,000 that were submitted.
Robert said: "It's gotten pretty overwhelming. I never dreamed when we started - we didn't even know that we would last - and then when it lasted and grew, it became huge. I never anticipated that it would get to this size."
Also showing are romance The Necessary Death Of Charlie Countryman, starring Shia LaBeouf and Evan Rachel Wood, Very Good Girls, starring Dakota Fanning and Elizabeth Olsen, and Kill Your Darlings starring Daniel Radcliffe as beat-poet Allen Ginsberg.
At the beginning of the festival calendar, Sundance has become the top US showcase for independent cinema and has played a huge role in creating opportunities for low-budget filmmakers to get their work made and seen.
Lynn Shelton, writer and director of Humpday and Your Sister's Sister, said: "It's almost like Burning Man. Once a year, this tiny little town that then transforms itself into kind of a crazy film city for 10 days out of the year. It's crammed with people all there for one reason. Whatever relationship they have to the industry, they're all there for the love of films."