Kissin was born in Moscow. He commenced his piano studies at age two, and entered the esteemed Gnessin School of Music for Gifted Children. He first studied there with Anna Pavlovna Kantor.
At the age of 10, Kissin made his orchestral debut and the year after that he gave his first recital in Moscow. Kissin's talents were manifested to the international scene in 1984, when he played Chopin's two piano concertos with the Moscow State Philharmonic.
On September 30, 1990, Kissin made his Carnegie Hall recital debut . Among many other pieces, he has recorded Sergei Rachmaninov's 2nd and 3rd piano concertos and Mozart's 12th and 20th piano concertos. He is considered by many musicians as one of the top pianists in the world.