Graduated from the Tchaikovsky Moscow State Conservatory.
Laureate of international music competitions, including, the International Tchaikovsky Competition (Moscow, 1974) and Leeds International Piano Competition (Great Britain, 1975) .
Не has performed with the Berlin Philharmonic, Chicago Symphony Orchestra, Philadelphia Orchestra, Israel Philharmonic, London Symphony and many other world renowned orchestras.
Alexeev has been a juror for a number of prestigious International Piano Competitions, including Tchaikovsky (Moscow), Van Cliburn (Texas), Chopin (Warsaw), etc.
He is Professor at the Royal College of Music in London as well as Honorary Professor of Central China Conservatory in Beijing.
His discography includes numerous recordings made for EMI, BMG, Virgin Classics, Hyperion, Brilliant Classics, Melodia etc.
Member of the jury of the International Television Contest for Young Musicians 'The Nutcracker', discipline ‘Piano’.