After beating Korchnoi in 2 matches in 1978 and 1981 and winning many tournaments, Karpov had to face a new powerful challenger - Kasparov. Kasparov was a very dynamic and active, sometimes even aggressive player who liked to take the initiative and attack, almost totally different from Karpov, who preferred positional and technical play.
They played 5 tough matches, every time with close results. The first time they met in 1984, in the match for the "world crown." Karpov was 12 years older, but he was not too old back then, 33, in his prime, and Kasparov was still young, 21, but had an Elo rating of 2710, slightly higher than Karpov with 2700.
The match was played in Moscow, from the 10th of September 1984 to the 15th of February 1985! After 5 months and 48 games (the previous record for the title match was Alekhine-Capablanca with 34 games), the match was abandoned, making it one of the most controversial in the world championships' history. The result was 5-3, with a record 40 draws! The winner should have been first to reach 6 wins like it was many times before in chess history. Only this time, something strange happened: too many draws! Karpov was leading 5-0 and he just needed one more win. But he couldn't deliver! Unbelievable. After many draws, Kasparov managed to win 3 games and cut the deficit to 3-5. He won the last 2 games before the match was stopped.
But then something extraordinary happened: FIDE president Florencio Kampomanes decided that it was enough, and he stopped the match, despite both players' wishes – they both wanted to continue. The reason was a concern about the players' health. So it became the first and only match that was abandoned without a winner.
It was decided to continue with another match in several months.
They started a new match in September 1985. To best of 24 games this time, to avoid what happened in the first one (all of the subsequent matches between them were played like this - best of 24 games). If this match finished in a draw, Karpov would retain his title. Because they started a new match, they started from zero, and because Karpov was leading in the first match, he was granted a rematch had he lost.
The match in 1985 was played from the 3rd of September to the 9th of November. Kasparov won closely by 13-11 (5-3, 16 draws) and became the youngest world champion by that time. He was 22.
After this, they would play 3 more matches, and every time it was a very close contest:
1986. Kasparov won 5-4, 15 draws
1987. Tie (Kasparov held the title) 4-4, 16 draws
1990. Kasparov won 4-3, 17 draws