The festival founder opened the event at Park City, Utah, and said "diversity is the point" of the independent film showcase, further evidenced by contributions from 32 countries and 51 first-time film-makers this year. Half of the films featured were made by women, for the first time.
The chorus of voices represented at Sundance "reflects the times we're in", the Hollywood star said.
"What Sundance stands for is giving new voices and new film-makers an opportunity to be seen and heard. We show what's there and what comes up will usually give you an indication of changing times."
Robert, along with festival director John Cooper and Sundance Institute director Keri Putnam, opened the 11-day festival with a news conference at the Egyptian Theatre in Park City, Sundance's home since 1981.
The films featured at the festival, like all art, reflect and inspired change, Robert said. "The festival, being as diverse as it is, shows all kinds of content, and that gives the audience a chance to choose," he said. "That's not quite so available in the main marketplace."
He revealed one of the most significant changes he has noticed over his years in film-making is the role sex plays on screen. Several of the festival films deal with sex.
"When I got into the film business in the early 60s, it was a romantic time. Sex and romance were pretty well tied together," Robert said. "Now, 40, 50 years later, we see that sexual relations have moved to a place where it doesn't feel like there's so much romance involved... Relations have changed, and they've changed because of changing times and because of new technology. People are texting rather than dating and all that kind of stuff.
"We just show what's there. We don't predict anything. We don't shape anything... We might be agents for change, but we're not shape-shifters. So there you have sexual relations and you look at how sex is treated today. It's just simply a reflection of the times we're living in and nothing more."