[2] His father Vyacheslav Yakovlevich Kuravlyov (1909–1979) worked as a locksmith at the Salyut Machine-Building Association and his mother Valentina Dmitriyevna Kuravlyova (1916–1993) was a hairdresser.

[3][4] In 1941 with the start of the Nazi invasion of the Soviet Union (known in Russia as the Great Patriotic War) his mother was arrested on false report, accused of counter-revolutionary activity (Article 58) and exiled to Karaganda, Kazakh SSR to work at the local plant.

[5] In five years she was freed without a right to live in Moscow and sent to Zasheyek, Murmansk Oblast in the Russian far north where she continued working as a hairdresser.

[11][12] His other notable roles of that period include Khoma Brut in one of the first Soviet horror movies Viy (1967),[13] antagonist Sorokin in a psychological melodrama Not Under the Jurisdiction (1969),[14] Robinson Crusoe in Stanislav Govorukhin's Life and Amazing Adventures of Robinson Crusoe (1972), a Nazi officer Kurt Eismann in Seventeen Moments of Spring (1973)[15] and Lavr Mironovich in Pyotr Todorovsky's The Last Victim (1975).

[21][22] According to Russian actress Lidiya Fedoseyeva-Shukshina, after being tipsy, Kuravlyov openly spoke about his negative attitude towards the leadership of the Soviet Union.

[26] In 2014 Kuravlyov along with 100 other Russian members of culture signed an open letter in support of Vladimir Putin's position regarding Ukraine and Crimea.