[2] At international level, Cherenkov made 34 appearances for the Soviet Union national team, scoring 12 goals.

[2] In his book on the history of Spartak, Robert Edelman [de] described him as "the longest-serving and most beloved of all Spartakovtsy":A native Muscovite, Fiodr Cherenkov (b.

Cherenkov was an enigmatic and fragile personality whose capacity for unexpected improvisation fit the Spartak image of the player as romantic artist.

A 2021 profile on BBC Sport relates that Cherenkov was a kind and approachable "regular guy" who could not understand his own fame.

He suffered several attacks of an unknown mental illness during his playing career, and missed important games because of it, but was "widely seen as the best Soviet footballer of the decade".