Natalia and partner are the 1980 ice dancing Olympic champions and two-time World champions. They skated for the Soviet Union throughout their competitive careers. They won their first medal at the senior level in 1974. They placed 4th at the 1974 Winter Olympics - the year ice dancing was introduced as an Olympic sport. Their success continued, and they were World champions in 1978 and 1979. They won the 1980 Olympics, but failed to defend their World title, making them the only team ever to unsuccessfully defend a World title after winning the Olympics.

In 1981 Linichuk and Karponosov retired from amateur competition. They got married on July 31, 1981. In February 1985 their daughter Anastasiya Karponosova was born. The couple lived in Moscow and later moved to Delaware. They now reside in Pennsylvania where they coach at the IceWorks Rink in Aston. It is common for ice dancing couples to be married, but rare for them to coach together. Linichuk and Karponossov have become successful ice dance coaches. They have coached many notable teams, including several notable Russian teams like, Angelika Krylova/Vladamir Federov and the Israeli team, Chait/Sakhnovsky. They also coached the Bulgarian World champions, Denkova/Staviski. Linichuk also works as a choreographer.