Kasparov was born Garik Kimovich Weinstein in Baku, Azerbaijan SSR (now Azerbaijan), Soviet Union.

From age 7, Kasparov attended the Young Pioneer Palace in Baku.

At 10 began training at Mikhail Botvinnik's chess school under noted coach Vladimir Makogonov.

Kasparov won the Soviet Junior Championship in Tbilisi in 1976, scoring 7 points of 9, at age 13.

He first qualified for the Soviet Chess Championship at age 15 in 1978, the youngest ever player at that level. He won the 64-player Swiss system tournament at Daugavpils on tiebreak over Igor V. Ivanov to capture the sole qualifying place.

In 1978, Kasparov participated in the Sokolsky Memorial tournament in Minsk. He had been invited as an exception but took first place and became a chess master. Kasparov has repeatedly said that this event was a turning point in his life, and that it convinced him to choose chess as his career. "I will remember the Sokolsky Memorial as long as I live", he wrote. He has also said that after the victory, he thought he had a very good shot at the World Championship.

His first win in a superclass-level international tournament was scored at Bugojno, Yugoslavia in 1982.

That year he joined the Communist Party of the Soviet Union (CPSU), as a member of which he was elected to the Central Committee of Komsomol in 1987.

The World Chess Championship 1984 match between Anatoly Karpov and Garry Kasparov had many ups and downs, and a very controversial finish. Karpov started in very good form, and after nine games Kasparov was down 4–0 in a "first to six wins" match. Fellow players predicted he would be whitewashed 6–0 within 18 games. In an unexpected turn of events, there followed a series of 17 successive draws, some relatively short, and others drawn in unsettled positions. Kasparov lost game 27 (5–0), then fought back with another series of draws until game 32 (5–1), earning his first-ever win against the World Champion.

Later in 1984, he won the Candidates' final 8½–4½ (four wins, no losses) against the resurgent former world champion Vasily Smyslov, at Vilnius, thus qualifying to play Anatoly Karpov for the World Championship.

In January 1984, Kasparov became the No. 1 ranked player in the world, with a FIDE rating of 2710. He became the youngest ever world No. 1, a record that lasted 12 years until being broken by Vladimir Kramnik in January 1996; the record is currently held by Magnus Carlsen.

In 1985, Kasparov played against thirty-two different chess computers in Hamburg, winning all games, but with some difficulty.

On October 22, 1989, Kasparov defeated the chess computer "Deep Thought" in both games of a two-game match.

In May 1990, Kasparov took part in the creation of the Democratic Party of Russia.

In 1991, Kasparov received the Keeper of the Flame award from the Center for Security Policy for "propagation of democracy and the respect for individual rights throughout the world". In his acceptance speech Kasparov lauded the defeat of communism while also urging the United States to give no financial assistance to central Soviet leaders.

Kasparov left the party on April 28, 1991, after its conference.

In December 1992, Kasparov visited Frederic Friedel in his hotel room in Cologne, and played 37 blitz games against Fritz 2 winning 24, drawing 4 and losing 9.

In June 1993, Kasparov was involved with the creation of the "Choice of Russia" bloc of parties and in 1996 took part in the election campaign of Boris Yeltsin. In 2001 he voiced his support for the Russian television channel NTV.

Kasparov cooperated in producing video material for the computer game Kasparov's Gambit released by Electronic Arts in November 1993.

In April 1994, Intel acted as a sponsor for the first Professional Chess Association Grand Prix event in Moscow played a time control of 25 minutes per game.

Kasparov played in a pair of six-game chess matches with an IBM supercomputer called "Deep Blue". The first match was played in Philadelphia in 1996 and won by Kasparov. The second was played in New York City in 1997 and won by "Deep Blue".

The Kasparov-Kramnik match took place in London during the latter half of 2000. Kramnik had been a student of Kasparov's at the famous Botvinnik/Kasparov chess school in Russia, and had served on Kasparov's team for the 1995 match against Viswanathan Anand.

In January 2003, he engaged in a six-game classical time control match with a $1 million prize fund which was billed as the FIDE "Man vs. Machine" World Championship, against "Deep Junior". The engine evaluated three million positions per second. After one win each and three draws, it was all up to the final game. After reaching a decent position Kasparov offered a draw, which was soon accepted by the Deep Junior team. Asked why he offered the draw, Kasparov said he feared making a blunder.

In June 2003, Mindscape released the computer game Kasparov Chessmate with Kasparov himself listed as a co-designer.

After winning the prestigious Linares tournament for the ninth time, Kasparov announced on 10 March 2005 that he would retire from serious competitive chess.

On 10 April 2005, Kasparov was in Moscow at a promotional event when he was struck over the head with a chessboard he had just signed. The assailant was reported to have said "I admired you as a chess player, but you gave that up for politics" immediately before the attack.

On 22 August 2006, in his first public chess games since his retirement, Kasparov played in the Lichthof Chess Champions Tournament, a blitz event played at the time control of 5 minutes per side and 3-second increments per move. Kasparov tied for first with Anatoly Karpov, scoring 4½/6.

In 2017, Kasparov came out of retirement to participate in the inaugural St. Louis Rapid and Blitz tournament from 14–19 August, scoring 3.5/9 in the rapid and 9/18 in the blitz, finishing 8th out of 10 participants, which included Nakamura, Caruana, former world champion Anand, and the eventual winner, Aronian.

Kasparov helped organize the Saint Petersburg Dissenters' March on 3 March 2007

Kasparov helped organize The March of the Dissenters on 24 March 2007.

In April 2007, it was asserted that Kasparov was a board member of the National Security Advisory Council of Center for Security Policy, a "non-profit, non-partisan national security [think tank in Washington, DC], which specializes in identifying policies, actions, and resource needs that are vital to American security".

On 14 April 2007, Kasparov led a pro-democracy demonstration in Moscow. Soon after the demonstration's start, however, over 9,000 police descended on the group and seized almost everyone. Kasparov, who was briefly arrested by the Moscow police, was warned by the prosecution office on the eve of the march that anyone participating risked being detained. He was held for some 10 hours and then fined and released.

On 30 September 2007, Kasparov entered the Russian Presidential race, receiving 379 of 498 votes at a congress held in Moscow by The Other Russia.

In October 2007, Kasparov announced his intention of standing for the Russian presidency as the candidate of the "Other Russia" coalition and vowed to fight for a "democratic and just Russia".

On 24 November 2007, Kasparov and other protesters were detained by police at an Other Russia rally in Moscow. 3,000 demonstrators arrived to allege the rigging of upcoming elections. Following an attempt by about 100 protesters to march through police lines to the electoral commission, which had barred Other Russia candidates from parliamentary elections, arrests were made. The Russian authorities stated a rally had been approved but not any marches, resulting in several detained demonstrators.

He was subsequently charged with resisting arrest and organizing an unauthorized protest and given a jail sentence of five days. Kasparov appealed the charges, citing that he had been following orders given by the police, although it was denied. He was released from jail on 29 November.

On 12 December 2007, Kasparov announced that he had to withdraw his presidential candidacy due to inability to rent a meeting hall where at least 500 of his supporters could assemble.

Kasparov actively coached Magnus Carlsen for approximately one year beginning in February 2009. The collaboration remained secret until September 2009.

Kasparov and Anatoly Karpov played a 12-game match from 21–24 September 2009, in Valencia, Spain.

Under Kasparov's tutelage, Carlsen in October 2009 became the youngest ever to achieve a FIDE rating higher than 2,800, and rose from world number four to world number one. While the pair initially planned to work together throughout 2010.

in March of that year it was announced that Carlsen had split from Kasparov and would no longer be using him as a trainer.

Kasparov was among the 34 first signatories and a key organizer of the online anti-Putin campaign "Putin must go", started on 10 March 2010.

In May 2010 he played 30 games simultaneously, winning each one, against players at Tel Aviv University in Israel.

In January 2011, Kasparov began training the U.S. grandmaster Hikaru Nakamura. The first of several training sessions was held in New York just prior to Nakamura's participation in the Tata Steel Chess tournament in Wijk aan Zee, the Netherlands.

Kasparov played two blitz exhibition matches in the autumn of 2011. The first was in September against French grandmaster Maxime Vachier-Lagrave, in Clichy (France), which Kasparov won 1½–½.

A little after that, in October 2011, Kasparov played and defeated fourteen opponents in a simultaneous exhibition that took place in Bratislava.

The second was a longer match consisting of eight blitz games played on 9 October, against English grandmaster Nigel Short. Kasparov won again by a score of 4½–3½.

On 17 August 2012, Kasparov was arrested and beaten outside of the Moscow court while attending the verdict reading in the case involving the all-female punk band Pussy Riot.

On 24 August, he was cleared of charges that he took part in an unauthorized protest against the conviction of three members of Pussy Riot. Judge Yekaterina Veklich said there were "no grounds to believe the testimony of the police". He could still face criminal charges over a police officer's claims that the opposition leader bit his finger while he was being detained.

In April 2013, joined in an HRF condemnation of Kanye West for having performed for the leader of Kazakhstan in exchange for a $3 million paycheck, saying that West "has entertained a brutal killer and his entourage" and that his fee "came from the loot stolen from the Kazakhstan treasury".

On 7 October 2013, Kasparov announced his candidacy for World Chess Federation president during a reception in Tallinn, Estonia, where the 84th FIDE Congress took place.

In early February 2014, Kasparov applied for citizenship by naturalization in Croatia, adding that he was finding it increasingly difficult to live in Russia.

On 28 February 2014, his application for naturalization was approved, and he is now a Croatian passport holder.

At the FIDE General Assembly in August 2014, Kasparov lost the presidential election to incumbent FIDE president Kirsan Ilyumzhinov, with a vote of 110–61.

On 25 and 26 April 2015, Kasparov played a mini-match against Nigel Short. The match consisted of two rapid games and eight blitz games. Kasparov won the match decisively with a score of 8½–1½, winning all five games on the second day.

On Wednesday 19 August 2015 he played and won the 19 games of a simultaneous exhibition in Pula, Croatia.

On Thursday 28 April and Friday 29 April 2016 at the Chess Club and Scholastic Center of Saint Louis, Kasparov played a 6-round exhibition blitz round-robin tournament with Fabiano Caruana, Wesley So, and Hikaru Nakamura in an event called the Ultimate Blitz Challenge.

On 2 June 2016, Kasparov played against fifteen chess players in a simultaneous exhibition in the Kaiser-Friedrich-Halle of Mönchengladbach. He won all games.