The Dominant Quartet was founded at the Gnessin Music Academy in Moscow in 1995 under the professorship of Valentin Berlinsky, the cellist of the Borodin Quartet.

In 1996, only a year after their foundation, the Dominant Quartet was awarded the Grand Prix at the Shostakovich International String Quartet Competition in St. Petersburg and subsequently joined the Moscow State Philharmonic Society.   This first success was soon repeated at the International String Quartet Competition in Boardeaux in 2001, where they were Prize Winners and awarded a "Prix du Ministere de la Cultura et de la Communication".

The Dominant Quartet has extensively toured Russia, Spain, Italy, France, Holland, Japan and Great Britain.   The Times described the quartet's UK debut in 2004 as "outstanding".   The quartet has performed at the Great Hall of the Moscow Conservatoire, the Concertgebouw in Amsterdam, the Suntory Hall in Tokyo, and London's Wigmore Hall.

They have made a number of recordings, mainly for Olympia and for the Moscow-based Art Classic label.