Anatoly Karpov became world chess champion in 1975 after defeating Viktor Korchnoi. Unfortunately, the world title had been left vacant by Bobby Fischer, who refused to defend it, and so there was a question mark over the legitimacy of Karpov's claim to the throne, despite the fact that he proceeded to rack up over 100 first prizes in tournaments over the following ten years.
Karpov defended his world title against Garry Kasparov in bizarre circumstances in 1984, when after 48 games the president of FIDE, Florencio Campomanes, called the match to a halt. Karpov had been leading by 5 wins to zero at one point, with 6 needed (from an unlimited number of games) to claim the title, when Kasparov changed his style of play and began to play for draws. There were a total of 40 draws in the match, and towards the end Kasparov began to win, bringing the score up to 5-3 in favour of Karpov when the match was abandoned, with Karpov's exhaustion being cited as the reason. The funny thing was, both players had stated that they wished to continue. Karpov was leading, only needing one more win, and Kasparov had found his form and considered that he was getting the better of his opponent. However, the wishes of the players did not seem to be at issue.
The match was resumed in 1985 at 0-0, with a new rule in place that the total number of games be limited to a maximum of 24, and Kasparov won after an intense struggle with the score standing at 13-11. Karpov played three separate rematches with Kasparov over the next few years, all of which he lost by the narrowest of margins.
More recently, the chess world championship cycle split in two, with FIDE and the Professional Chess Players' Association (PCA) running separate championships, each claiming to be the 'legitimate' title. Garry Kasparov was the PCA title holder until his recent loss to Vladimir Kramnik, but Karpov managed to win the FIDE title from Gata Kamsky, thereby becoming world champion again, though no one doubted that Kasparov had the more valid claim, due to the fact that he has never lost a match to Karpov. Karpov lost the title again recently to Viswanathan Anand.
Karpov's style of play was often compared to that of Tigran Petrosian, being focused on positional dominance and control rather than tactical attacking play. This gave his matches with Kasparov an epic quality, as their styles are almost totally opposite, as are their personalities, Kasparov being aggressive, arrogant and outspoken, and Karpov being calm, studious and pleasant. He was unfairly regarded as being boring, and did admit to being a keen stamp collector. He once played a chess/snooker match with the then world snooker champion Steve Davis, with predictable consequences on both sides.