Under the tutelage of head coach Jackie Sherrill, May and his teammates led Pitt to a 39–8–1 four-year record, which included three top-10 finishes and four bowl games. The university retired May's jersey number (73) in 2001, and May became the eighth Pitt player to be so honored. He was inducted into the College Football Hall of Fame in 2005, becoming the 23rd Pitt player or coach to earn the honor.
In 1981, May donated $10,000 to Pitt's alumni sports fund to give back to the university.
The Washington Redskins drafted May with the 20th pick of the first round of the 1981 NFL Draft, and he played guard for the Redskins from 1981 to 1990. He was a member of the famed "Hogs" offensive line, which was instrumental in the Redskins' victories in Super Bowl XVII and XXII (though May was injured for Super Bowl XVII). He was named one of the 70 greatest Redskins of all time. May started 115 games for the Redskins. He missed the 1990 season due to a knee injury.
May's work as a football analyst has recently come under fire from some fans who claim that May presents biased opinions against their teams. Most notably May has been criticized for his opinion that the Ohio State Buckeyes were overrated and were not worthy of being in the first college football playoff. May remains silent on allegations that he is biased against Big Ten football teams. Recently, Lou Holtz was asked: "if you had to guess, where does May's opinion on the Big Ten come from?" Holtz told the reporter that he would have to ask May.
In January 1979, as a sophomore at Pitt, May was arrested for disorderly conduct, resisting arrest, criminal mischief, inciting a riot, and making terroristic threats. May reportedly was jumping on top of parked cars, threatening police officers and encouraging a crowd of onlookers to fight the officers. He was found guilty of criminal mischief and disorderly conduct, while the other charges were dismissed.
As a member of the Redskins, May was twice arrested for DUI. The second instance occurred in March 1990, and the first in 1985 in Arlington, Virginia.