From 1998 Alexei Raev studied in the Merzlyakov Institute at the Tchaikovsky Moscow State Conservatory under R. P. Matiyakin. Between 2001 and 2006, he studied at the Gnesin Russian Academy of Music under the Distinguished Artist of Russia, Professor V. S. Shish. In 2008 he completed his Assistatship-Internship. In 2013, he completed the graduate program in Production at the Gnesin Russian Academy of Music with distinction.
In 1998 he was admitted to the scene orchestra of the Bolshoi Theater of Russia. From 2002 on he has been the concertmeister of the French horn group of the main orchestra of the Bolshoi Theater of Russia. Simultaneously, he was a soloist at the Russian National Orchestra under the direction of M.V. Pletnev between 2000 and 2004, and at the Russian National Philharmonic Orchestra under the direction of V. T. Spivakov between 2004 and 2007.
In 1997 he became the Laureate of the international competition of young wind instrument performers.
In 2000 he became the first prize Laureate of the All-Russia Rimsky-Korsakov open competition of wind and percussion instrument performers (St. Petersburg).
In 2003 he became the Laureate of the Yamaha scholarship prize.
In 2012 he became the Laureate of the Board of Trustees of the Bolshoi Theater of Russia.