Friðrik's best result in World Chess Championship competition was in the 1958 Interzonal tournament, where he finished equal 5th–6th, automatically earning the grandmaster title (the first for Iceland) and qualifying for the 1959 Candidates Tournament, the last stage to determine the challenger to the World Chess Champion in 1960.

Among his other best tournament results were joint third in the first Piatigorsky Cup, Los Angeles 1963, with 7½/14 and shared first with Ljubomir Ljubojević at Wijk aan Zee 1976, ahead of Mikhail Tal.

[2] Olafsson continued to play occasionally into the 21st century, winning a rapid match against fellow veteran Bent Larsen in 2003 by a score of 5–3.

[4] In 1978, Olafsson succeeded Max Euwe as president of the international chess governing body FIDE.

Olafsson delayed the planned September 19 start date of the match in a bid to get the Soviets to release Korchnoi's son.