Ali Aliev was born in Tashkent to a Crimean Tatar family; they had been forcibly exiled to the Uzbek SSR as special-settlers (official second-class citizens) along with most of the Crimean Tatar population in the Surgun of May 1944. Despite numerous hardships, in 1973 his father Enver became a Hero of Socialist Labour for cotton production, but subsequently faced reprimand from party leaders for endorsing a letter requesting right of return to Crimea and was only able to return to his homeland in 1990.