Meskhi has won five singles and doubles titles on the WTA Tour.

She has also won one singles and two doubles titles on the ITF Women's Circuit.

On 5 August 1991, she reached her best singles ranking of world No.

Her best performance at a Grand Slam tournament came when she got to the quarterfinals of the 1990 US Open, defeating Akiko Kijimuta, Natasha Zvereva, Katia Piccolini and Linda Ferrando before losing to eventual champion Gabriela Sabatini in straight sets.

This biographical article relating to Georgian tennis is a stub.