Babakova won an Olympic bronze medal in Atlanta 1996 and became World Champion in Seville 1999. She also won four other World Championship medals, with bronzes in 1991 and 1995 and silvers in 1997 and 2001. Track and Field News magazine ranked her in the world's top ten in their annual merit rankings for 13 out of 14 seasons (1991-2004), the exception being 1998. She was in the top five ten times. Only Stefka Kostadinova, among other female high jumpers, has more top ten rankings. Her 2.01 m clearance in Oslo on her 36th birthday in 2003 is the women's W35 World Record.