Conway's off-Broadway credits include One Flew Over the Cuckoo's Nest, One for the Road, The Elephant Man, Other People's Money, and When You Comin' Back, Red Ryder?, for which he received the 1974 Drama Desk Award.
[3] On Broadway, Conway appeared in Indians, Moonchildren, and in revivals of The Plough and the Stars, Of Mice and Men (as George Milton, opposite James Earl Jones as Lennie Small), and Dinner at Eight.
[3] In his first major screen role, Conway portrayed Roland Weary in the 1972 film Slaughterhouse-Five, based on the Kurt Vonnegut novel.
He played the fictional Buster Kilrain in Ron Maxwell's Civil War Duology: Gods and Generals and Gettysburg.
He guest starred on The Good Wife episodes "Threesome",[a] "Boom", [b] and "Wrongful Termination"[c] as Jonas Stern, a founding partner of the titular character's law firm.