He made his stage and screen debut in mid 1970's as schoolboy. In 1982-1984 Yefremov served in Soviet Army. In 1987 he graduated from the Moscow Art Theatre School.

Yefremov was married four times, has six children. His first wife was the editor Asya Vorobieva, their son Nikita Efremov is a Sovremennik Theatre actor. His second wife was the actress Evgeniya Dobrovolskaya, their son Nikolay Efremov is also an actor. His third wife was actress Kseniya Kachalina, they have a daughter Anna Mariya. His fourth wife is audio engineer Sofiya Kruglikova, they have daughters Vera and Nadezhda, and son Bori.

From 2009 on Yefremov presents Channel One show Zhdi Menya (1998), dedicated to search of long lost relatives and friends.

In 2010's he collaborated Dmitry Bykov over their project "Citizen Poet" (a pun on Nikolai Nekrasov's poem "Poet and Citizen"). Yefremov reads poems, written by Bykov, which are usually satirical comments on the contemporary Russian society, politics and culture. Each poem parodies the style of a famous poet of the past, e.g. Pushkin, Nekrasov, Kipling, among others. It was originally broadcast on Dozhd TV channel, but the original project was closed, because the poems were too critical towards Russian government. Currently, the show is hosted in audio format by Echo of Moscow radio station.