Along with her two younger sisters, she was coached in chess by her father, Laszlo Polgar. In 1991, she became the first woman to earn the men's grandmaster (GM) title in the normal way (by achieving three GM "norms" - Nona Gaprindashvili and Maia Chiburdanidze had earlier been made GMs on account of them being women's world champions).
Unlike her sister Judit, Zsuzsa has participated in woman's events, and won the Women's World Championship in 1996. Following that, FIDE did a couple of unusual things in the women's chess scene that had a dramatically negative effect on Zsuzsa. 1) She was denied the right to defend her title under FIDE auspices, 2) All active women players were given 100 bonus elo rating points except her (since Zsuzsa has played in many mixed men-women events -- her playing strength can be considered comparable to a male player of similar elo rating, but most of the other "strong" women players tend to play more exclusively in women's events, thus continuing to carry forward this arbitrary 100 point rating inflation.)
Throughout most of her career, Zsuzsa has been either the best or second best woman chess player (behind her sister Judit Polgar.) In more recent events other female players such as Xie Jun have shown similar playing strength.