He was born, educated and started his career in Fife, but his peak playing years were in the early 1960s with the Glasgow club Rangers, whom he helped to win ten trophies between 1960 and 1965, and where he became known as "Slim Jim".

However, he started drinking heavily during a four-month layoff caused by a leg fracture in December 1964, his fitness suffered, and he was transferred to Sunderland in summer 1965.

From 1960 to 1967, he was a leading member of a strong Scottish international team that lost only once to England, in 1966, shortly after he recovered from the leg fracture.

In the 1967 match against England, who had won the 1966 World Cup, he taunted the opposition by ball juggling while waiting for his teammates to find good positions.

After retiring from football he became manager of a pub, and his continued heavy drinking damaged his liver so badly that he needed two transplants at the age of 55, after which he swore off alcohol.

After he died of pancreatic cancer in 2001, his funeral was held in Glasgow Cathedral and his ashes were buried at Rangers' Ibrox Stadium.

[7] His former headmaster James Carmichael took an interest in ex-pupils and encouraged Baxter to join local football team Halbeath Juveniles instead of one of the glamour clubs.

[15] In December 1964, Baxter played brilliantly to set up a 2–0 win for Rangers in an away game against Rapid Vienna in the European Cup.

With the game won, rather than play out time Baxter's confidence over-extended into arrogance to make fun of his opponents with the ball.

Nottingham Evening Post reporter Tony Pritchett described the signing of Baxter as "probably the worst transfer in Forest's history".

[22] In the 1963 game Scotland were reduced to 10 men when their left back Eric Caldow's leg was broken in a tackle by Bobby Smith – substitutions were not allowed at that time.

[24] The following year Scotland, again inspired by Baxter and Law, beat England 1–0, and only poor finishing prevented them from scoring a bigger win.

[8] In the 1967 British Home Championship, Baxter produced a dominating but controversial performance for Scotland, tantalising England, who had won the World Cup in 1966,[8] by playing "keepie uppie" (ball juggling) while waiting for teammates to get into good positions.

[25] Some commentators accepted that humiliating the opposition was a valid objective, while others regarded it as childish and thought Scotland should have won a more convincing victory than the actual 3–2 scoreline.

[28] In October 1963, which may have been Baxter's best year overall, he played for the "Rest of the world" in a match against England to celebrate the centenary of The Football Association.

Scottish public opinion at the time blamed lack of commitment by the "Anglos", Scottish-born players who spent little or none of their playing careers in Scotland.

His close friends included the Celtic players Billy McNeill, Pat Crerand and Mike Jackson, in defiance of the unwritten rule that rivals did not associate.

[8][35] Like some other British football stars of the late 20th century, Baxter drank to excess,[12][36] and at one point was said to be consuming three bottles of Bacardi a day.

[7][12] Later in his life, when asked if earning the huge incomes of footballers in later decades would have made a difference, he replied, "Aye, I would have gambled £50,000 a week on the horses instead of £100.

"[37] In February 2001, Baxter was diagnosed as suffering from cancer of the pancreas, and he died at his home on Glasgow's South Side on 14 April 2001, with his partner Norma and his sons Alan and Steven at his bedside.

[12] His funeral was held in Glasgow Cathedral, where a reading was given by Gordon Brown, a long-time fan of Raith Rovers F.C., where Baxter began his career.

[25] Indeed, although Rangers insisted that players tuck their shirts completely into their shorts, Baxter always let part of his dangle over his left hip.

[38] Baxter played most of his best football in his early twenties, before the leg fracture against Rapid Vienna in December 1964 and the start of his heavy drinking that made his nickname "Slim Jim" less appropriate.

[8] After the replay of the Scottish Cup Final against Celtic in 1963 he stuffed the match ball up his shirt and later gave it to a new member of the team.

[45] The Tartan Army unsuccessfully attempted to get the new Wembley Stadium footbridge named after him,[46][47] and on 24 February 2005 Scottish National Party MP Pete Wishart presented an Early Day Motion in the House of Commons supporting this campaign.