Swilling played for the Georgia Tech Yellow Jackets. Swilling set the NCAA record for sacks in a game, with seven against North Carolina State and the Georgia Tech mark for sacks in a season (15). Voted first-team All-America in 1985, Swilling left Georgia Tech as the all time sack leader and now ranks 5th.
Swilling was traded to the Detroit Lions in 1993 for draft picks. In order to sign Swilling Detroit had to "unretire" the legendary Joe Schmidt’s number 56. In his first year with Detroit he made it to his fifth and final Pro Bowl. The Detroit Lions qualified for the playoffs in both of Swillings' seasons with the team, being eliminated each time, in the first round, by the Green Bay Packers. Swilling finished his career with 107.5 sacks.
Swilling lost all six playoff games he played in; no other player in NFL history has more losses without a win.