Alekseyeva was inducted into the inaugural class of the Women's Basketball Hall of Fame in 1999.
On 24 February 2012, Alekseyeva was announced as a member of the Naismith Memorial Basketball Hall of Fame Class of 2012; she was formally inducted on 7 September.
While playing with the senior USSR National Team, she won the gold medal at the EuroBasket Women, in 1950, 1952, 1954, and 1956.
Specifically, they won the Summer Olympic Games gold in 1976 and 1980, the FIBA World Championship for Women in 1964, 1967, 1971, 1975, and 1983 (the USSR boycotted the 1979 tournament), and the EuroBasket Women in 1962, 1964, 1966, 1968, 1970, 1972, 1974, 1976, 1978, 1980, 1981, and 1983.
Alekseyeva's husband, Evgeny Alekseev, was also a well-known basketball player and coach.