He began his musical career in the 1970s, but did not garner popular recognition until the 2000s when he became one of the most important artists of the Russian progressive rock scene.

At the same time, Kostarev worked with many Russian jazz and rock musicians as a session guitarist, one of them being Sergey Letov.

In the 2000s Kostarev started performing solo and gained popularity as one of the most important Russian progressive rock figures.

In the year 2006 Alexander Kostarev received a special invitation to lead the Jam session that concluded the first day of the InProg 2006 festival.

At the same year the Kostarev Group song "Who's Flying Over Me" appeared on the "Theme of Appreciation: A Worldwide Tribute to Eddie Jobson" compilation.