Glenn attended Riverdale High School, where he was a two-way lineman and a teammate of Will Rackley. Regarded as a four-star recruit by Rivals.com, Glenn was listed as the No. 16 offensive guard prospect in the class of 2008.
College career
As a true freshman, Glenn appeared in 13 games making 10 starts, and was named to College Football News′s All-Freshman First Team. Glenn ranks tied first all-time at UGA in career starts by an offensive lineman with 50, of which 28 were at left guard, 18 at left tackle and four at right guard.
Glenn was selected by the Buffalo Bills in the second round. Glenn became the ninth player from the University of Georgia to be drafted by the Buffalo Bills. On September 9, 2012, Glenn started at left tackle and helped block for a rushing attack in which C.J. Spiller rushed for a career-high 169 yards against the New York Jets. Glenn became first Bills rookie to start at left tackle in a season opener since Glenn Parker in 1990. On September 16, 2012, Glenn and his offense did not allow a sack for the second straight week against the Kansas City Chiefs. It was the second time in team history the offensive line held opponents to zero sacks in the first two games of a season. The last time was during the 1980 season. On November 11, 2012, Glenn was part of an offense that produced season bests of 481 total yards and a time of possession of 33:50 against the New England Patriots. At the end of the 2012 season, Glenn started all 13 games he played. Glenn was part of an offensive line that held opponents to 30 sacks, while blocking for a rushing attack that averaged 138.6 yards per game. On November 3, 2013, Glenn started at left tackle for an offensive line that did not give up a sack or quarterback hit and blocked for a rushing attack that recorded a season-high 241 yards rushing against the Kansas City Chiefs. At the end of the 2013 season, Glenn started all 16 games for the first time in his career. Glenn blocked for just the second Bills running back duo in franchise history to exceed 800 yards a piece on the ground. Glenn started all 16 games for the second time in his career in 2014, and he would accomplish the feat again in the 2015 season. On May 3, 2016, Glenn agreed to terms with the Bills on a five-year contract extension worth $65 million. Glenn's 2017 season was plagued by foot and ankle injuries, only playing six games before being placed on injured reserve on December 15, 2017.
Cincinnati Bengals (2018–present)
On March 12, 2018, the Bills agreed to trade Glenn, the 21st overall pick in the 2018 NFL draft, and a 2018 fifth round pick to the Cincinnati Bengals in exchange for the 2018 12th overall pick and a 2018 sixth round pick. The deal became official on March 14, 2018, at the start of the NFL year. He was named the Bengals starting left tackle, starting 13 games, missing three due to injury. After drafting Jonah Williams in the first round in 2019, Glenn was moved to left guard. However, he was moved back to left tackle after Williams suffered a season-ending injury. On September 13, 2019, Glenn was ruled out for Week 2 after suffering a concussion during the Bengals' 2nd preseason game. On October 18, 2019, he was suspended for week 7 by the Bengals for disciplinary reasons related to treatment for his concussion. He was activated from suspension on October 21, 2019. Glenn was released on March 13, 2020.