She won those Grand Slam doubles titles with four different partners: Gigi Fernández, Martina Hingis, Pam Shriver, and Larisa Savchenko Neiland.

In addition to her Grand Slam doubles titles, Zvereva teamed with Meskhi to win a bronze medal at the 1992 Olympics in Barcelona.

Nevertheless, in 1988, at the age of 17, she made her sole Grand Slam singles final at the French Open beating Martina Navratilova en route.

Zvereva is one of the few players to have beaten both Graf and Monica Seles, both former world number ones, in the same Grand Slam singles tournament.

Ten years later at Wimbledon in 1998, Zvereva defeated the fourth-seeded Graf in the third round 6–4, 7–5 and the sixth-seeded Seles in a quarterfinal 7–6, 6–2.

Starting with the French Open in 1987 and extending through Wimbledon in 2000, Zvereva played in 51 of the 54 Grand Slam singles tournaments held, reaching the quarterfinals or better eight times.