His roles have included Bill Lester in She Came to the Valley (1979), Pfc Glenn Kelly in Nashville (1975), Wes Hightower in Urban Cowboy (1980), astronaut Alan Shepard in The Right Stuff (1983), Emmett in Silverado (1985), Captain Bart Mancuso in The Hunt for Red October (1990), Jack Crawford in The Silence of the Lambs (1991), John Adcox in Backdraft (1991), Bill Burton in Absolute Power (1997), Roger in Training Day (2001), Ezra Kramer in The Bourne Ultimatum (2007), Chris Chenery in Secretariat (2010), Kevin Garvey Sr. in the HBO series The Leftovers (2014–2017), and as Stick in the Marvel Cinematic Universe series Daredevil (2015–2016) and The Defenders (2017).

He joined George Morrison’s acting class, helping direct student plays to pay for his studies and appearing onstage in La MaMa Experimental Theatre Club productions.

Two of Glenn's early television roles were as Hal Currin in the 1966 crime series Hawk, starring Burt Reynolds, and Calvin Brenner on the CBS daytime serial The Edge of Night.

In 1978, Glenn left Los Angeles with his family for Ketchum, Idaho, and worked as a barman, huntsman, and mountain ranger, occasionally acting in Seattle stage productions.

That same year, he tried his hand at gangster movies when he starred as the real-life sheriff turned gunman Verne Miller in the movie Gangland: The Verne Miller Story, which was given a theatrical release only in Finland and went straight to video in the U.S.[citation needed] In the beginning of the 1990s, Glenn's career was at its peak as he appeared in several well-known films, such as The Hunt for Red October (1990), The Silence of the Lambs (1991), Backdraft (1991), and The Player (1992).

Later, he gravitated toward more challenging movie roles, such as in the Freudian farce Reckless (1995), tragicomedy Edie & Pen (1997), and Ken Loach's sociopolitical declaration Carla's Song.