Gurevich won the Ukrainian Chess Championship in 1984[4] and became USSR Champion in 1985, controversially taking the title from co-winners Alexander Chernin and Viktor Gavrikov on tiebreak points' This was after a three-way playoff had been organized and all the game results were draws.

He took first at Reggio Emilia 1989, ahead of Vassily Ivanchuk, Jaan Ehlvest and Viswanathan Anand and tied for first at Moscow 1990 with Alexander Khalifman and Evgeny Bareev.

He placed 8th at the 2005 FIDE World Cup, beating Robert Markus, Pavel Eljanov, Alexei Shirov and Vladimir Malakhov along the way, before losing to the eventual winner, Levon Aronian.

In 2006, playing top board for his second adopted nation, Turkey, at the Turin Olympiad, he registered a respectable 58%.

In 1991, he wrote a book on the latter, entitled Queen's Indian Defence: Kasparov System, published by Batsford.

In the Fourth ACP World Rapid Cup knockout tournament, held 27–29 May 2010 in Odesa, Ukraine, Gurevich created a sensation after beating two grandmasters, each rated at over 2700.