Garry Kimovich Kasparov (Russian: Га́рри Ки́мович Каспа́ров, Russian pronunciation: [ˈɡarʲɪ ˈkʲiməvʲɪtɕ kɐˈsparəf]; born Garik Kimovich Weinstein, 13 April 1963) is a Russian (formerly Soviet) chess grandmaster, a former World Chess Champion, writer, political activist, considered by many to be the greatest chess player of all time.

Kasparov became the youngest ever undisputed World Chess Champion in 1985 at the age of 22 by defeating then-champion Anatoly Karpov. He held the official FIDE world title until 1993, when a dispute with FIDE led him to set up a rival organization, the Professional Chess Association. He continued to hold the "Classical" World Chess Championship until his defeat by Vladimir Kramnik in 2000. He was the first world champion to lose a match to a computer under standard time controls, when he lost to Deep Blue in 1997.

Kasparov's ratings achievements include being rated world No. 1 according to Elo rating almost continuously from 1986 until his retirement in 2005 and holding the all-time highest rating of 2851. He was the world No. 1 ranked player for 255 months, by far the most of all-time and nearly three times as long as his closest rival, Anatoly Karpov. Kasparov also holds records for consecutive tournament victories and Chess Oscars.

Vladimir Borisovich Kramnik (Russian: Влади́мир Бори́сович Кра́мник; born 25 June 1975) is a Russian chess grandmaster. He was the Classical World Chess Champion from 2000 to 2006, and the undisputed World Chess Champion from 2006 to 2007. He has also won the two strongest tournaments (by rating strength) in chess history: the 2009 Mikhail Tal Memorial and the 2010 Grand Slam Masters Final. He has won three team gold medals and three individual medals at Chess Olympiads.

In October 2000, he defeated Garry Kasparov in a match played in London, and became the Classical World Chess Champion. In late 2004, Kramnik successfully defended his title against challenger Péter Lékó in a drawn match played in Brissago, Switzerland. In October 2006, Kramnik, the Classical World Champion, defeated reigning FIDE World Champion Veselin Topalov in a unification match, the World Chess Championship 2006. As a result Kramnik became the first undisputed World Champion, holding both the FIDE and Classical titles, since Kasparov split from FIDE in 1993. In 2007, Kramnik lost the title to Viswanathan Anand, who won the World Chess Championship tournament ahead of Kramnik. He challenged Anand at the World Chess Championship 2008 to regain his title, but lost.

Sven Magnus Øen Carlsen (born 30 November 1990) is a Norwegian chess Grandmaster and chess prodigy who is currently the number-one ranked player in the world. In January 2010 he became the seventh player in history to be ranked number one in the world on the official FIDE rating list. His peak rating is 2835, the second highest in history, after Garry Kasparov.

On 26 April 2004 Carlsen became a Grandmaster at the age of &1000000000000001300000013 years, &10000000000000148000000148 days, making him the third-youngest Grandmaster in history. On 1 January 2010 the new FIDE rating list was published, and at the age of &1000000000000001900000019 years, &1000000000000003200000032 days, he became the youngest chess player in history to be ranked world number one, breaking the record previously held by Vladimir Kramnik. Carlsen was also the 2009 World blitz chess champion.

His performance at the September–October 2009 Nanjing Pearl Spring tournament has been described as one of the greatest in history and lifted him to an Elo rating of 2801, making him the fifth player to achieve a rating over 2800 – and aged 18 years 10 months at the time, by far the youngest to do so.

Robert James "Bobby" Fischer (March 9, 1943 – January 17, 2008) was an American chess Grandmaster and the 11th World Chess Champion. He is widely considered one of the greatest chess players of all time. Fischer was also a best-selling chess author. 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 Chess960 is gaining in popularity.

A chess prodigy, at age 13 Fischer won a "brilliancy" that became known as The Game of the Century. Starting at age 14, he played in eight United States Championships, winning each by at least a point. At age 15½, he became both the youngest grandmaster and the youngest candidate for the World Championship up to that time. He won the 1963–64 U.S. Championship 11–0, the only perfect score in the history of the tournament. In the early 1970s he became one of the most dominant players in modern history—winning the 1970 Interzonal by a record 3½-point margin and winning 20 consecutive games, including two unprecedented 6–0 sweeps in the Candidates Matches. According to research by Jeff Sonas, in 1971 Fischer had separated himself from the rest of the world by a larger margin of playing skill than any player since the 1870s. He became the first official World Chess Federation (FIDE) number-one rated chess player in July 1971, and his 54 total months at number one is the third longest of all time.