Anna Dmitrieva was born in an artistic family. Her father was the chief artist in MKhAT and her mother was an actress. Her father died when she was seven years old, and her mother married for the second time a popular composer Kirill Molchanov. Anna started playing tennis at the age of 12. In less than a year she won Moscow junior championships as a member of the Dynamo team, and the next year she became also Moscow junior singles champion. At the age of 16 she was allowed to play at senior tournaments, and in a year she became champion of Moscow in singles, women's doubles and mixed doubles. In 1958, when the USSR joined the International Tennis Federation, Anna Dmitrieva became a member of the first Soviet delegation at the Wimbledon Championships. She reached the final of the junior girls' tournament. In 1958–1967, Dmitrieva won 18 titles in Soviet championships: five times in singles, nine in women's doubles and four times in mixed doubles. In 1959, 1961, 1962 and 1964 she won the championships in all three categories. Dmitrieva also won open championships of Czechoslovakia and Hungary, Uganda, Yugoslavia. In 1965 she won Scandinavian Indoors championship in women's doubles and reached finals in singles. She also won women's tournament at the Queen's Club in 1963 and Wimbledon Ladies Plate in 1965. She won a number of amateur tournaments in Africa from 1964 to 1968 and the Games of the New Emerging Forces in Jakarta in 1963. At the Grand Slam tournaments, her highest success was reaching Wimbledon doubles semis in 1963 with Judy Tegart; they lost to the eventual champions Maria Bueno and Darlene Hard. At the Wimbledon Championships, Dmitrieva also reached the quarterfinals twice in ladies' doubles and in mixed doubles in 1967 when she and Alexander Metreveli played the longest game in the tournament's history against Bueno and Ken Fletcher. Dmitrieva also played in the French Open doubles quarterfinals in 1968. After finishing her player's career in the late 1960s, Dmitrieva worked as a tennis coach for four years and then became a sports journalist and commentator for the Soviet TV and radio. Today, she is the director of sports channels department at NTV Plustelevision network. Dmitrieva won a number of professional awards during her career as a sports journalist; in particular, she was named the best sports journalist of the Russian TV in 1997, and in 2008 she won another prize for life achievement in this field.
