His debut novel was a thriller called Valge kuningriik (The White Kingdom, 2006). It won the Betti Alver Prize for best first novel. His second novel was a work of historical fiction, set in the time of the First Crusade. This novel called Palveränd (The Pilgrimage, 2008) won the EU Prize for Literature and was translated into several languages subsequently (e.g. Italian, Hungarian, and Finnish). In 2011, he published a third novel Kindel linn (Stronghold). Palveränd and Kindel linn are the first and second part of what is to become a trilogy.
His first play Leegionärid (Legionaries), about the fallen soldiers of the Estonian Legion, appeared in 2010 and premiered in 2013 in Rakvere. It received the Virumaa Literary Award in 2011. Another historical play, Kuningad (Kings) was published in 2014 and is about the murder of the four Estonian kings during the St. George's Night Uprising (1343).
Aleksejev lives in Tallinn.