Fischer's victory qualified him for the 1958 Portorož Interzonal. He tied for 5th–6th, which sufficed to advance him to the Candidates Tournament to decide the challenger to World Champion Mikhail Botvinnik. It also made him, at 15, the youngest grandmaster ever - a record that stood until Judit Polgar broke it in 1991. At the Candidates tournament, held in Bled/Zagreb/Belgrade, Yugoslavia, Fischer finished fifth out of eight, the top non-Soviet player.

Fischer won the US Championship all eight times he played, in each case by at least a point. In the US Championship 1963/64 (1963) he achieved the only perfect score (11-0) in the history of the tournament.

In 1962, he won the Stockholm Interzonal 2½ points ahead of Efim Geller and Tigran Vartanovich Petrosian. This made him one of the favorites to win the Candidates Tournament at Curaçao, but he only finished fourth, behind Petrosian, Geller, and Paul Keres.

In a famous article in Sports Illustrated, The Russians Have Fixed World Chess, Fischer accused the Soviets of cheating: Petrosian, Geller, and Keres had drawn all 12 of the games among themselves at Curaçao. Because of this, he refused to play in the next Candidates cycle. He did play in the 1967 Sousse Interzonal, but left it while leading, because of a scheduling dispute occasioned by Fischer's refusal to play on Saturday, his Sabbath.

In 1970 he won the Palma de Mallorca Interzonal by a record 3½ points. The following year, he shocked the chess world by sweeping the Fischer-Taimanov Candidates Match (1971) and the Fischer-Larsen Candidates Match (1971) by identical 6-0 scores. He also won the first game of his Candidates final against former World Champion Tigran Vartanovich Petrosian, giving him a modern record of 20 consecutive wins at the highest level of competition. He beat Petrosian by 6½-2½ to advance to the World Championship match against reigning champion Boris Spassky. This also gave him a FIDE rating of 2785, making him at that time the highest-rated player in history.

In Reykjavik, he won the Fischer-Spassky World Championship Match (1972) by 12½-8½ to become the 11th World Chess Champion. In 1975, Fischer forfeited his title after FIDE refused to meet his conditions for a World Championship match with Anatoly Karpov. He then vanished from the public eye for nearly 20 years.

After ending his competitive career, he proposed a new variant of chess and a modified chess timing system. His idea of adding a time increment after each move is now standard, and his variant "Fischerandom" (or "Chess960") is gaining in popularity.(2)

Fischer resurfaced in 1992 to play a match against his old rival Spassky in Yugoslavia, which he won 10-5 with 15 draws. This action allegedly violated U.S. Treasury Department regulations that forbade transacting business with Yugoslavia. Fischer evaded authorities for twelve years until July 13, 2004, when he was arrested in Japan. On March 22, 2005, he was granted Icelandic citizenship and finally freed from Japan. He died of renal failure in Iceland on January 17, 2008 at the age of 64.

Fischer's anthology, My 60 Memorable Games, was published in 1969. It has been described as a "classic of objective and painstaking analysis"1 and is regarded as one of the great classics of chess literature.

(1) Hooper & Whyld. The Oxford Companion to Chess. 1992

(2) Wikipedia article: Bobby Fischer