She befriended Ekaterina Furtseva, the powerful Soviet Minister of Culture, and was reputed to be a favourite singer of Leonid Brezhnev. Among her many honours were the Lenin Prize (1970) and Order of Lenin (1979) as well as the titles of People's Artist of the USSR (1973) and Hero of Socialist Labour (1987). According to Dmitri Shostakovich, Zykina was "more than a brilliant interpreter, she was a coauthor, co-creator of composers". Her signature songs include Techot Volga and Orenburgskii platok. An asteroid (4879 Zykina) is named after her.
