After earning his associate's degree, Muren began working as a visual effects Artist full-time. In 1976, Muren was hired at Industrial Light & Magic (ILM), then an upstart visual effects studio founded by George Lucas. Lucas' and ILM's first film, Star Wars, was released in 1977 to wide critical and public acclaim and was the highest-grossing film of all time up until that point. In 1985 he worked on the visual effects of the Disney theme park’s Captain EO the American 3D/4D science fiction film starring Michael Jackson, directed by Francis Ford Coppola and the executive Producer was George Lucas.

Muren, along with Steve Williams and Mark Dippé, helped to usher in a new age of computer generated imagery with the CG dinosaurs of Jurassic Park (1993). Steven Spielberg had intended to use go-motion for the dinosaurs, but quickly changed his mind when shown a test of a CG T-Rex (with Marin County as the backdrop).

In June 1999, Muren was honored with a star on the Hollywood Walk of Fame, the first visual effects Artist to ever be so recognized. He has also been a recipient of nine Academy Awards for Best Achievement in Visual Effects and a Technical Achievement Academy Award, the most of any living movie-maker.

Jurassic Park was the breakthrough that convinced George Lucas that Technology had advanced enough to make the Star Wars prequels. Director Peter Jackson was similarly inspired by Jurassic Park's technical breakthrough to begin planning and pre-production on the Lord of the Rings trilogy and King Kong (2005). Muren also contributed effects work on two Jurassic Park sequels: The Lost World: Jurassic Park (1997) and Jurassic World (2015).