They began to skate together in 1965 at the ages of 24 and 23 under the direction of Igor Moskvin. Despite the unusually late start, the pair turned out to be a success. Skating in pairs, Tamara Moskvina and Alexei Mishin became the National Champions in 1969, European silver medalists in 1968 and bronze medalists in 1969. In 1968, they  finished fifth at the Olympic Games in Grenoble.  Their major achievement, however, was the second place at the World championships a year later. 
"We spent our practices laughing, being very friendly and understanding each other's problems," Moskvina recalls.
Having, Ludmila Belousova and Oleg Protopopov (who were known for the beauty of their classical style) as the main competitors, Moskvina and Mishin took a different approach to their skating. 
"Classical music opens unlimited possibilities, but in our time it just didn't make sense to try competing with Ludmila Belousova and Oleg Protopopov by using the same classical style, beautiful lines, exact movements and poses. That niche clearly belonged to them. That's why our coach, Igor Moskvin, suggested a program that made us look much better. It suited our skating perfectly and gave us a unique look. Back then it was taken by many as bit avant garde but it would look quite normal now," says Mishin. 
"Mishin and I weren't tall and with our build we wouldn't have made a very nice classical pair, so we did modern style. We skated to French and folk music, those kinds of programs," adds Tamara Moskvina.

In 1970, Tamara Moskvina and Alexei Mishin split to start coaching careers and both have reached an extraordinary level of success.