Luke was born and raised in Michigan where he went on to play college hockey for his home state at the University of Michigan. He played four seasons for the Wolverines and was named an alternate captain in just his sophomore season. He was named captain for his junior and senior seasons and finished his college career by posting a career high 10 goals and 11 assists as a senior. After being passed over in the NHL Entry Draft, Luke signed a contract with the Grand Rapid Griffins of the AHL where he made his professional debut. During his time in Grand Rapids, he helped the Griffins win their first Calder Cup. Following the 2012-13 season, Luke was signed by the Detroit Red Wings. He made his NHL debut for the Red Wings on October 12, 2013. On March 10, 2020, Glendening played in his 500th career NHL game for the Red Wings, becoming the first undrafted player to do so for Detroit since the NHL went to a seven-round draft in 2005. After 8 seasons with the Detroit Red Wings, Luke signed a two-year deal with the Dallas Stars in 2022.