[3] His first notable student was Sergey Volkov who excelled at compulsory figures and was the first Soviet skater to win the men's World title.

Although a singles coach, Kudriavtsev has also worked with a few pairs, including Lyudmila Smirnova / Andrei Suraikin.

[3] Early in his coaching career, Kudriavtsev worked at a rink in Sokolniki, then at Kristal in Luzhniki, followed by Olimpiyski, and finally Moskvich.

[3] He runs summer training camps in Moscow and in Films, Switzerland and many international skaters, including Stéphane Lambiel, Lina Johansson, Oscar Peter and Jamal Othman, have trained under him there.

In 2014, he returned to coach Michael Christian Martinez, the first figure skater in a tropical zone for the 2014 Winter Olympics.