She won her first world medal, a bronze on balance beam, at the 1987 World Championships. She went on to compete in the 1988 Olympic Games in Seoul, South Korea, where she won four medals: gold in the team competition, gold on vault, silver on floor, and bronze in the individual all-around.

Just three days after the Olympics, Boginskaya’s longtime coach, Lyubov Miromanova, committed suicide. Miromanova had been a surrogate mother to Boginskaya, coaching and caring for her after she moved from Minsk to train full-time in Moscow. After her death, Boginskaya began training with Tatiana Grosovivich. Under Grosovivich’s tutelage, Boginskaya became world champion in 1989 and later dedicated her performance to her late mentor.

In 1990, Boginskaya became the third woman to sweep the European Championships, winning the gold medal in every individual event. The only other gymnasts to do so were Věra Čáslavská, Larisa Latynina, and Ludmilla Tourischeva. In doing so, she defended her titles in the all-around, vault, and floor exercise, and added titles in the uneven bars and balance beam. In 1991, in a controversial finish, Boginskaya lost the gold medal in the all-around to Kim Zmeskal of the United States. However, she earned gold medals in the team and balance beam competitions.

In 1992, Boginskaya, then 19 years old, had a disappointing performance at the 1992 European Championships, falling on her final event, the floor exercise. She finished in fifth place, while her young teammate Tatiana Gutsu won the all-around title. Boginskaya won the balance beam title with a score of 9.95 and remained a favorite to win the all-around title at the 1992 Summer Olympics in Barcelona, Spain.

After the 1992 Olympics, Boginskaya appeared alongside her compatriot Vitaly Scherbo in the music video for the song “Revolution Earth,” by The B-52’s.

Boginskaya retired after the 1992 Olympics but decided to make a comeback in 1995. She said that she was inspired by Katarina Witt who had made a memorable comeback of her own at the 1994 Winter Olympics. Boginskaya moved to Houston, Texas, to train with Bela Karolyi and upgraded the difficulty of her routines. In 1996, at age 23, she placed second in the all-around at the American Cup to one of Karolyi’s pupils, Kerri Strug, as well as at the European Championships in Birmingham, behind the defending world all-around champion (and future Olympic all-around champion), Lilia Podkopayeva of Ukraine. She then progressed to the 1996 Olympics in Atlanta, Georgia, where she was one of a number of “older” gymnasts competing. She led the Belarus team to sixth place and competed in the all-around and vault finals, but won no individual medals, placing 15th in the all-around and fifth on vault.

Boginskaya is among a small group of women to have competed in three Olympic Games; and due to the break-up of the Soviet Union, she competed at each Games under a different flag: USSR, the Unified Team, and Belarus. She was inducted into the International Gymnastics Hall of Fame in 2005.