Female chess players in the modern era generally compete in a mix of open and women's tournaments. With women representing a low fraction of all chess players throughout history, it has been uncommon for women to win open tournaments where women and men are mixed together, particularly at the higher levels. Championship tournaments, both at adult and youth levels, are even rarer for women to win in part because women and men are typically divided into different sections at these events, heavily reducing the number of female players competing against male players.
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María Teresa Mora was among the first notable instances of a woman winning an open tournament, becoming Cuban national champion in 1922. Mora was the only student of José Raúl Capablanca, the World Champion at the time. Vera Menchik's 1926 victory at the Hastings Major Reserve, a tier below the highest master level, is regarded as the first high-level tournament victory by a woman. Nona Gaprindashvili is credited with the first elite tournament victory by a woman, winning the Lone Pine International more than 50 years later in 1977. It was this victory that led her to become the first woman to earn the Grandmaster (GM) title a year later. The next Women's World Champion, Maia Chiburdanidze, was the first woman to win an elite round-robin tournament, winning two in the mid-1980s. Her second such victory, in Banja Luka, was mostly against other GMs.
Judit Polgár, widely acknowledged as the greatest female chess player in history, has won the most high-level open tournaments among women by far. Some of her strongest victories in classical came in the four-player double round-robin Crown division in Hoogeveen, where she won four times and regularly faced competition averaging near or above 2700-level. The strongest ten-player elite round-robin tournaments (known as super-tournaments) won by women were the 1994 Madrid Torneo Magistral and 2000 Japfa Classic in Bali by Judit Polgár, and the 2017 Biel Grandmaster Tournament by Hou Yifan. All of these tournaments featured opposition above 2600-level on average. The biggest and strongest Swiss tournament victory by a woman was the 2016 London Rapid Superplay in which Valentina Gunina claimed the title in a field of 475 players, facing an opposition rated over 2500 on average. In classical Swiss events, Gaprindashvili's 1977 success at Lone Pine and Sofia Polgar's 1989 "Sack of Rome", in which she scored 8½/9 against mostly GMs at age 14, are the strongest and most notable victories.
The only two world championships won by women were both by Judit Polgár, who was the 1988 U-12 World Youth Champion and the 1990 U-14 World Youth Champion. Humpy Koneru was the U-12 Asian Youth Champion in 1999. At adult levels, the highest-level national championships won by women were the 1991 Hungarian national championship by Judit Polgár, the 2000 Lithuanian national championship by Viktorija Čmilytė, and the 2006 Austrian national championship by Eva Moser. Ketevan Arakhamia-Grant, the oldest woman to earn the GM title, has won the Scottish national championship three times.
