Polgár is the only woman to have won a game from a current world number one player, and has defeated nine current or former world champions in either rapid or classical chess: Anatoli Karpov, Garry Kasparov, Boris Spassky, Vasily Smyslov, Veselin Topalov, Viswanathan Anand, Ruslan Ponomariov, Alexander Khalifman, and Rustam Kasimdzhanov.

Also in 1988, Polgár won the under-12 " Boys " section of the World Youth Chess and Peace Festival in Timişoara, Romania.

Going into the last round Polgár needed only a draw to achieve the GM title, but she won her game against GM Tibor Tolnai to win first place with six points in nine games.

In the summer of 1994, Polgár had the greatest success of her career to that point, when she won the Madrid International in Spain.

Despite being closely matched in ratings, Polgár won the match 6 – 2.

Polgár won two, drew one and lost one and won $ 12, 000 in prize money.

In October 1998, Polgár won the VAM four-grandmaster tournament in Hoogeveen, Netherlands by 1½ points over Jan Timman.

Anand won the tournament in a tie-break game over Polgár.

In January 2000, Polgár had, for her, a disappointing result in a tournament in Pamplona, Spain, which was won by Nigel Short.

Polgár had another disappointing result later in the month in the category XVIII tournament in Corus Wijk aan Zee which was won by Kasparov.

In April and May 2000, Polgár won one of the strongest tournaments ever held in Asia.

Going into the last round four players, Polgár, Khalifman, Karpov and Gilberto Milos were tied, but Polgár won her game over Braziliam GM Milos while Khalifman and Karpov played against each other in a draw.

In June 2003, Polgár finished tied for third with Boris Gelfand, in the Enghien-les-Bains International Tournament in France, scoring 5½ – 3½, behind Evgeny Bareev who won the tournament and GM Michael Adams.

In October 2003, Polgár won the 4 – grandmaster Essent tournament in Hoogeveen, Netherlands.

The tournament, which was now considered by some as the most important in Europe, was won by fellow Hungarian Péter Lékó while Polgár scored 7 / 13 to tie for fourth with Alexander Grischuk, Michael Adams and Kramnik.

Polgár tied with Boris Gelfand with 9½ points and won her individual game against Viswanathan Anand, at the time the world's No. 2 player.

In July 2007, Polgár played in the Biel Chess Festival which was won by 16-year-old Magnus Carlsen.

The tournament was won by Bu Xiangzhi of China, whose only loss was to Polgár.

Despite being younger, 25 to Polgár's 33 years, and higher rated, 2708 to Polgár's 2682, Navara was crushed by Polgár who won the match 6 – 2.

In November 2010, Polgár won the four-player rapid tournament which was held to celebrate the National University of Mexico's 100th anniversary.

Polgár won a close opening match against Vassily Ivanchuk.

The tournament, of 393 players of which 167 were Grandmasters, was won by Russian Vladimir Potkin on tie-break, GM Radosław Wojtaszek won the silver, while Polgár placed third, winning the bronze.

In late February and early March 2001, Polgár played in the elite Linares double round-robin invitational of six of the world's strongest players.

In October 1988, Polgár finished first in a 10-player round-robin tournament in London, scoring 7 – 2, for a half point lead over Israeli GM Yair Kraidman.

In September 1992, Polgár participated in a tournament held in Aruba in which a team of senior men's players competed against a team of top women players.

Polgár then tied for first in the Hastings tournament held over New Years, 1992 – 93.

Immediately following the Hastings tournament, Polgár played an exhibition match in February against former World Champion, Boris Spassky.

Polgár also participated in the Melody Amber tournament in Monaco which featured a blindfold tournament of 12 grandmasters.

In 1993, Polgár became the first woman to ever qualify for a Men's Interzonal tournament.

In September 1995, Polgár finished third in a tournament in the Donner Memorial in Amsterdam, behind Jan Timman and Julio Granda Zuniga who tied for first.

The tournament marked the first time the 17-year-old Polgár was invited to compete with the world's strongest players.

Although Polgár recovered by the end of the tournament, she went into a slump over the next six rounds, gaining only half a point.

In August 1996, Polgár participated in a very strong 10 – player tournament in Vienna.

Polgár finished in clear fifth position in the 12-GM tournament, ahead of Anand, Ivanchuk, Gelfand and Shirov.

Polgár handed co-winner Vishwanathan Anand his only loss of the tournament.

In November 1998, Polgár played in the Wydra Memorial Rapid chess tournament in Israel.

In October 1999, Polgár participated in the four-player GM section of the VAM Chess tournament in Hoogeveen, Netherlands.

Jan Timman lead early in the tournament, but Polgár staged a comeback scoring 3 points in the last 4 games to share first place.

However, Polgár drew both her games with Kasparov, the first time in her career she had done this under tournament time controls.

In June 2001, Polgár finished fourth in the European Championship in Ohrid, Macedonia, a 13-round Swiss-system tournament of 143 Grandmasters and 38 IMs.

In 2003, Polgár scored one of her best results: an undefeated clear second place in the Category 19 Corus chess tournament in Wijk aan Zee, Netherlands, just a half-point behind future World Champion Viswanathan Anand, and a full point ahead of then-world champion Vladimir Kramnik.