Glenn joined Tottenham Hotspur as a schoolboy apprentice in 1974. His senior debut came in February 1976 when he immediately announced his arrival with an impressive goal against Stoke City and England goalkeeper Peter Shilton. He also scored on his full international debut against Bulgaria in November 1979.

The 1979–80 season was seen as his major breakthrough year. The 22-year-old midfielder scored 19 goals in 41 league appearances and was deservedly awarded the PFA Young Player of the Year. Glenn was described as one of the most talented footballers of this generation. ‘His sublime balance and close control, unrivalled passing and vision and extraordinary shooting ability, both from open play and set pieces, made Hoddle the most gifted English player of his generation.’

In 1981 he starred as Spurs won the FA Cup and in the following season they retained the trophy after Glenn scored in both the Final and Final replay.
He moved to AS Monaco in 1987 to play under the guidance of Arsene Wenger. His team-mates included SEM Hall of Famer George Weah. They immediately inspired the club to the 1988 League title and the quarter-finals of the European Cup.

Glenn had further spells at Swindon Town and Chelsea before ending his playing career. He played 53 times for England during his international career, scoring 8 goals.
Since retirement from playing the game, Glenn has had several jobs in management including a spell at Chelsea and his old side Tottenham Hotspur. He guided England to qualification for the 1998 World Cup and his 60% win rate during his spell as manager is only bettered by Sir Alf Ramsey and Fabio Capello.

In 2008 Glenn set up the GHA Academy. It is the first independent, professional football academy, offering an alternative to the professional club system. The Academy is based at the Montecastillo Resort in southern Spain.

Alongside his work with the Academy scholars, Glenn appears regularly in the Sky Sports studio as a pundit, covering Premier League and Champions League games.