Dreev’s chess career began when he was young winning making tournaments including World Under-16 in 1983 and 1984, and the European Junior Champion in 1988. In 1989, he became a grandmaster and made his first appearance in the Russian Championship. At the 2004 Russian Championship, he placed third while legendary Garry Kasparov won the event. He has participated the world championship cycles and FIDE World Championship tournaments (1999, 2000, 2001, and 2004). His best tournament victories were at the 1995 Biel Grandmaster Tournament and at the 1995 Hoogovens tournament. Other tournament victories include the 2000 European Blitz Chess Championship, 2007 Parsvnath Open in New Delhi, 2008 Magistral Casino de Barcelona round-robin tournament, 2011 Cento Open, and the 2012 European Rapid Chess Championship in Warsaw. Dreev has also represented Russia in five Chess Olympiads between 1992 and 2004, with the Russian team winning gold medals in 1992, 1994, and 1996, and silver in 2004.