In 1978 he won the Sokolsky Memorial in Minsk. In 1979, without a FIDE rating, he won an international tournament in Banja Luka, Yugoslavia with 8 wins and 7 draws. This was his first international tournament. His first FIDE rating was 2500.

In 1980 he won at Baku with 8 wins and 7 draws, qualifying for the Grandmaster title. He then won the World Junior Championship five months later at the age of 17.

In 1981 he was second, behind Karpov, at Moscow. He then tied for first place with Psakhis in the USSR Championship at Frunze.

In 1982 he won at Bogojno with 6 wins and 7 draws. He then won the Moscow Interzonal with 7 wins and 6 draws, thus becoming a Candidate for the world championship. He won the chess oscar for 1982.

In 1983 he won at Niksic, then defeated Beliavsky and Korchnoi in the Candidates matches. He won the chess oscar for 1983.

In 1984 he defeated Smyslov in their Candidates match and became the challenger for the world championship. On September 10, 1984 Kasparov and Karpov began their marathon match in Moscow. The match was for the first to win 6 games. After 3 wins, 40 draws, and 5 losses, FIDE President Campomanes stopped the match after 5 months of play. In 1984 Kasparov gave the first satellite simultaneous exhibition as he played players in London and New York.

The Kasparov-Karpov match was halted on February 15, 1985. On Septermber 3, 1985 Kasparov and Karpov resumed their match in Moscow. This time, Kasparov won with 5 wins, 16 draws, and 3 losses. The match had been limited to 24 games. Garry Kasparov became the youngest world chess champion at age 22 years, 210 days on November 9, 1985. He won the chess oscar for 1985.

On July 25, 1986 Kasparov defended his title against Karpov in London, then in Leningrad. Kasparov won with 5 wins, 15 draws, and 4 losses. Kasparov won at Brussels (OHRA) later that year. Kasparov won the chess oscar for 1986.

In April, 1987 Kasparov tied for first at Brussels (SWIFT) with Ljubojevic. On October 12, 1987 Kasparov defended his title in Seville, Spain against Karpov. He retrained his title by drawing the match with 4 wins, 16 draws, and 4 losses. He won the chess oscar for 1987. His FIDE rating was 2750.

In 1988 Kasparov won at Amsterdam, Belfort, and Reykjavik. In August, he tied for first with Karpov at the USSR championship. In 1988 he was doing commercials, thus becoming the first Soviet in Western commercials.

In 1989 Kasparov won at Barcelona, Skelleftea (tied with Karpov), Tilburg, and Belgrade. Kasparov won the Grand Masters Association World Cup for 1988-89. His FIDE rating peaked at 2810 in 1989, the highest ever recorded. He also defeated Deep Thought computer in a two game match in new York.

In February, 1990 Kasparov took first place at Linares, Spain. In October he again defended his title against Karpov. They played their match in New York and Lyons, France. Kasparov won the match with a score of 12.5 - 11.5 and won $1.7 million.

In 1991 Kasparov won at Tilburg, a Category 17 tournament with the average rating of 2666. Kasparov became the first registered user of ChessBase in 1991.

In 1992 Kasparov won at Paris.

In March, 1993 Kasparov won at Linares, Spain. This was a Category 18 event, with 11 of the top 14 players in the world participating. In March, 1993 Kasparov declined to play for the world chess championship organized by FIDE. FIDE forfeited Kasparov as the World Champion as Kasparov founded the Professional Chess Association. In September, Kasparov began his PCA World Championship match in London against Nigel Short. Kasparov won the match with a score of 12.5 - 7.5.

In 1994 Kasparov lost to Fritz 3 in a blitz event in Munich.

In 1995 Kasparov won at Riga and Novgorod. In September he began his Intel-PCA World Championship match with Anand in New York. He won the match with 4 wins, 13 draws, and 1 loss. In November, Kasparov won the Paris Intel Grand Prix. Later, he defeated Fritz 4 in London with one win and one draw. In December, Kasparov played 10 players over the Internet, winning 7 and drawing 3.