The striker Conny Torstensson began his career at Åtvidabergs FF, who was considered a great talent of football in Sweden. From 1967 to 1973 he played for this club in the first league. In his final two seasons, he was Swedish Champion. In Europe Champions Cup Åtvidaberg met in the first round to the German champions FC Bayern Munich ( Munich ) won the first leg 3-1. In the return game led Åtvidaberg - thanks to two goals Torstenssons - already 3-0 before Uli Hoeness scored the first goal. In the penalty shootout, Bayern prevailed 4-3 and Torstensson joined at the behest of coach Udo Lattek and Manager Robert Swan for 580,000 German marks still in the winter break to Munich. With Torstensson, Bayern have won in the course for the first time the European Cup of Champions, where he was employed in both finals. Since Torstensson was until 1977 under contract, he won the European Cup twice more; because it thereby important goals (10 in 21 games ) shot, he was nicknamed "Mr. European Cup ".
Torstensson completed for Bayern 81 league (11 goals), twelve DFB Cup ( 4 goals) and both World Cup games. His first competitive goal for Bayern was the 2-1 victory in the second round of the Club Cup with Werder Bremen on 15 December 1973. His Bundesliga debut Torstensson (18th Round ) on 5 January 1974 the 2:4 defeat Fortuna Dusseldorf; his first goal was a 1-0 winner at Rot-Weiss Essen on January 19, 1974 ( 20th Round ). In 1977 he moved to Switzerland for a year in the A- division club FC Zurich National, returned to his former club and ended after three seasons in 1980 his career.
Torstensson played 1972-1979 40 times for the national team and scored seven goals. He participated in the 1974 World Cup in Germany, where he, in the group B of the second final round three times came in the group III of the first final round twice to insert and against Yugoslavia with the 2-1 victory four minutes from the end, was responsible for the only victory in this round. In 1978 he participated again at the World Cup in Argentina in part, but which was disappointing for him and his team, as it was eliminated in the preliminary round ( 1-1 against Brazil, 0-1 against Austria and Spain).
- World Cup winners in 1976
- European Cup Winners ' Cup in 1974, 1975, 1976
- German Cup: 1974
- Swedish Cup winners 1970, 1971
- Swedish Champion 1972, 1973