Crum is a 1957 graduate of Mount Union College in Alliance, Ohio and received a master's degree from Case Western Reserve University.
After graduation, Crum was a teacher and assistant football coach at several high schools in Ohio, including Boardman, Sandusky, and Warren Harding.
After the 1977 season, Crum accepted the head coaching position at North Carolina and was replaced by Tom Reed.
Crum was hired as head coach at the University of North Carolina at Chapel Hill in 1978, succeeding Bill Dooley.
At North Carolina, Crum coached a number of future NFL players, including Lawrence Taylor, Harris Barton, Reuben Davis and Kelvin Bryant.
He was the winningest coach in school history until Mack Brown (in his second tenure at North Carolina) surpassed him after a game against Duke in 2019.