Rangers played a total of 61 competitive matches during the 1978–79 season. The early season league form was terrible as the team failed to win any of the first six league matches but a run was put together. Things began to unravel, however, as leadership of the league evaporated. The team had to settle for second place behind champions Celtic. The pivotal match was a 4-2 Old Firm defeat a Parkhead. There was success for Greig in the national cup competitions. Victory in the 1979 Scottish Cup Final over Hibernian required a second replay to separate the sides before Rangers eventually won 3-2. The 1979 Scottish League Cup Final ended in a 2-1 win for Rangers over a strong Aberdeen with goals from Alex MacDonald and Colin Jackson.

Wallace's treble-winning team of the previous season performed well in the European Cup. Rangers eliminated Juventus after defeating the Italians 2–1 on aggregate - the first time Rangers had ever recovered from a first-leg defeat to win a two-legged European tie. Dutch side PSV Eindhoven, the then UEFA Cup holders, were overcome in the next round (the club's first home defeat in European competition), before an injury-stricken Rangers side lost to Cologne at the quarter-final stage.

All results are written with Rangers' score first.

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