Anatoly Fedyukin began to actively engage in handball while studying at the institute in Voronezh but, in order to continue his sports career, he moved to Moscow. He went on to win the USSR Championship five times and, at the 1976 and 1980 Olympics, scored 21 goals in eight games. Fedyukin won 103 international caps and scored 222 goals for the national team, and won a gold medal at the 1982 World Championships in West Germany. After this championship, Fedyukin became a coach in Moskva, Voronezh and, between 2000-02, was head coach of the Icelandic club Fram. In 2006 he was appointed director of the center of the Moscow Department of Education. In his later years, he actively played billiards.