This year will mark the 26th anniversary of the Sundance Institute, which Redford founded to help independent film makers break into the business.
Now, having a film showcased at Sundance is a definite status symbol, something that Redford obviously relishes as he gets older. This year, Redford will turn 70. He can hardly believe it.
"I can't, honest to God," Redford said. "I'm not being falsely this or that, It's hard for me to - I can't get a hold of that."
Redford also said that throwing himself into Sundance has taken a toll on his own film career.
"I have not been able to do as many films as I'd like to make because of a commitment to Sundance that grew larger than I imagined and when you commit, you commit," he said.
Redford found inspiration for the name of the Sundance Film festival in his 6,000 acre retreat high in the mountains of Utah.
"It was a pretty tough name to beat," he told Sunday Morning correspondent Rita Braver. "I tried all kinds of other names and finally, I thought, 'You know you have to into the fact that it is just a great name.'"
The 1969 film, "Butch Cassidy and the Sundance Kid" is considered a classic. Redford starred as Sundance and Paul Newman as Butch: a pair of loveable outlaws.
But not many people know that Redford almost didn't get the part. There was talk about giving Marlon Brando the part.
"I think I was the - I was so much the last choice," he said. "No, I was, that they tried everything to keep me out of the picture because I wasn't known compared to Paul."
His role as the Sundance Kid changed all that. Redford, who'd grown up in California, then went to Europe to study art and fell into acting, was suddenly a big star and life became very different.
"Suddenly you realize that you were being treated like an object and the danger to your psyche is that if you didn't pay attention and you didn't stay clear," Redford said. "You would begin to behave like one and if you did that too long you might end up becoming one. You know, So I thought you'd better look out for that."
Redford made some calculated choices. While he continued to star in mainstream movies like "The Way We Were" and "The Great Gatsby," there were also smaller films like "Downhill Racer" and "The Candidate." It was Redford who personally pushed to get "All The President's Men" made, where he and Dustin Hoffman played the investigative reporters, Bob Woodward and Carl Bernstein, who uncovered the Watergate scandal.
"It took four years, and the studio, they said 'Politics? I don't think so,'" Redford said. "'You know, Watergate is a dead issue.' And I said, 'Its not. It's a detective story about investigative journalism and about the American trait of hard work and hard work led to something that spared us the lost of our first amendment. That to me is worth making."