[1] Monroe was chosen by the Sox in the first round of the 1974 Major League Baseball draft with the eighth overall selection.

He made his big league debut on August 23 against the Detroit Tigers, throwing two scoreless, hitless innings of relief.

He started that day's game against the California Angels, going five innings, giving up six hits and four runs (three earned), and walking two to take the loss.

When Adrian Garrett replaced Vern Law as manager of the Denver Zephyrs in 1984, Monroe was brought in to become pitching coach.

Monroe was an integral part of the advanced scouting team, which aided the Chicago White Sox in winning the 2005 World Series.