As the U.S. embassy in Tehran was being stormed, they escaped and found refuge in the home of the Canadian ambassador.
In this film, based on real events, the plan to save lives involves a fake Canadian film crew making a fake movie called "Argo."
Ben Affleck is the film's director, the star and a producer.
"This is the absolute apex of my career thus far," Affleck said. "I feel this is the movie -- and I've never said this before -- this is the best movie that I have ever been involved with. I'm enormously proud of it."
Apparently, Affleck isn't the only person who feels that way.
"When you have 100 people telling you it's the best movie they've seen in years, you start to think, well, maybe it's going to be fairly successful," said Alan Arkin.
The film also has the ability to elicit a wide response from viewers.
"It's a great movie to watch with an audience," said John Goodman. "I mean, the reactions that you get, the communal feeling, it's just terrific."
For Affleck, this film brings up feelings from another one of his famous movies.
"I haven't felt this proud or this excited since 'Good Will Hunting,'" he said. "And when I made 'Good Will Hunting,' you know, I had no idea what I was talking about."
"Argo" opens Oct. 12.