He is also a member of the Scotland Football Hall of Fame, which honours the best players to play in Scotland and is located in the Scottish Football Museum. In 1982 he captained Scotland to victory in the UEFA European Under-18 Championship, the only major trophy won by any Scottish national football team. He captained each of the Scotland teams from under-16 level through under-18, under-20, under-21 and senior level. McStay made his full national team debut in 1983. He represented Scotland 76 times, including appearances at two World Cups in 1986 and 1990, during a 14-year international career. McStay was also selected for two UEFA European Championships in 1992 and 1996, but withdrew from the latter because of an ankle injury. In 2010, he moved to live in Sydney, Australia with his wife Anne Marie and their six children. McStay now runs Maestro Sports, a startup software company specialising in sport coaching and management. McStay's great-uncles Jimmy and Willie McStay were former Celtic captains, and his brothers Willie and Raymond also played for Celtic. Their father John worked as a scout for the club. One of his sons, Chris, has played football for Sutherland Sharks in Australia and for Clyde in Scotland. His nephew John (Willie's son) played with Celtic Boys Club before moving onto Motherwell under-19s and later played for Ayr United as a defender before becoming a Celtic academy coach. His cousin Jock McStay played for Raith Rovers during the 1990s, and Jock's son Jonny played at Junior level in the 2010s.