After a large preliminary round victory over Sion of Switzerland, the Dons knocked out Dinamo Tirana of Albania and Lech Poznan of Poland to set up a quarter final tie with the West Germans Bayern Munich.
After a 0–0 draw in Munich, Aberdeen fell behind early on at home in the second leg before Neil Simpson equalised.
In the semi-finals, Belgian team Waterschei of Genk were beaten 5–2 over two legs, and put Aberdeen into the final.
Thousands of fans made the trip from Aberdeen to Gothenburg in Sweden to see the Scottish Cup holders play the Spaniards Real Madrid.
In a wet evening at the Ullevi Stadium, Aberdeen won 2–1 after extra time to win their first European trophy.