Showing a diverse range on stage and usually cast as tough guys and working blokes on TV and film, Conway has been toiling for more than 25 years in all three media, becoming one of those faces people recognize on the street, but whose name may prove elusive. He trained with famed coach Uta Hagen, and scoring his first success in the New York and Stockbridge, MA, production of "When You Comin' Back, Red Ryder?" (1973). He Went on to co-star in many prestigious productions including "Of Mice and Men" with James Earl Jones, "The Elephant Man" (as Dr. Treves) and "Other People's Money".
Conway made his feature film debut in the forgettable "Believe in Me" (1971) and subsequently portrayed the sullen Weary in "Slaughterhouse Five" (1972). He subsequently co-starred as gangsters opposite Sylvester Stallone in "F.I.S.T." and "Paradise Alley" (both 1978). After appearances in a few undistinguished films (e.g. "The Funhouse" 1984, "Flashpoint" 1984), he made his feature directorial debut with the political drama "El Sol y la Luna/The Sun and the Moon" (1987) which starred his wife, Mila Burnette. He was the doctor who suggested sterilization to cure Laura Dern's problems in Martha Coolidge's "Rambling Rose" (1991) and was Sgt. Buster Kilrain, one of the few non-officers featured in the epic "Gettysburg" (1993). Conway co-starred with Sharon Stone and Gene Hackman in Sam Raimi's "The Quick and the Dead" (1995).
Conway was already playing second leads in 70s TV-movies, such as "The Deadliest Season" (CBS, 1977) and "Johnny, We Hardly Knew Ye" (NBC, 1977), but in the 80s he became a frequent player in TV longforms with key roles in such efforts as "Sidney Sheldon's 'Rage of Angels'" (NBC, 1983) and the acclaimed "Something About Amelia" (ABC, 1984). He also played Chillingworth opposite Meg Foster's Hester Prynne in the PBS miniseries "The Scarlet Letter" (1979) and co-starred with Bruce Davison in the first PBS TV-movie "The Lathe of Heaven" (1980). He reprised his stage role of Dr. Frederick Treves opposite Philip Anglim's "The Elephant Man" (ABC, 1983). Conway won higher profile roles in the 90s with the Disney Channel movie, "The Whipping Boy" (1994) and "Larry McMurtry's 'Streets of Laredo'" (CBS, 1995).