He played three matches against Kasparov for the title from 1986 to 1990 before becoming FIDE World Champion once again after Kasparov broke away from FIDE in 1993. The next major meeting of Kasparov and Karpov was the 1994 Linares chess tournament. In 2002 he won a match against Kasparov defeating him in a rapid time control match 2½–1½.
For his decades-long standing among the world's elite Karpov is considered one of the greatest players of all time. He had a peak Elo rating of 2780 and his 90 total months at world number one is second all-time behind only Garry Kasparov since the inception of the FIDE ranking list in 1970.