Introduced to gymnastics at age five by her grandmother, Podkopayeva competed internationally for the first time at the 1993 World Championships. The following year, she won her first title at the European Championships, coming first in the floor exercise. At the 1995 World Championships, Podkopayeva became the winner of the all-around competition and the horse vault, winning two silver medals as well.
After winning the European all-around title as well in early 1996, Podkopayeva was certainly one of the favourites for the gold medal at the 1996 Summer Olympics. After three events in the all-around final, 6 gymnasts still stood a chance of winning the event. An excellent performance on the floor moved Podkopayeva from third to first place to become the first female gymnast to win the Olympic all-around title as a defending World Champion since Lyudmila Turishcheva in 1972. She dedicated her title to her grandmother, who had passed away just three weeks prior to the Olympics. In the same event in which she won the all-around, the floor exercise, she won a second gold medal. In the balance beam, she also earned a silver medal.