Volkov played professionally for Stroitel (1981–1986; 1988–1989), CSKA Moscow (1986–1988), Atlanta Hawks (1989–1992), Panasonic Reggio Calabria (1992–1993), Panathinaikos (1993–1994), Olympiacos (1994–1995), and Kyiv (2000–2002).

In the USSR, he was also selected MVP in 1989, and was one of the key players on the Soviet national team since 1985, winning the gold medal at the 1988 Seoul Games.

In 1986, he was drafted by the Atlanta Hawks in the 6th round, together with CSKA Moscow teammate Valeri Tikhonenko.

His brief career in NBA was hampered by injury as well as competition from several all-star front-men: Dominique Wilkins, Kevin Willis and Moses Malone.

After missing the whole next season, he came back stronger, roughly doubling his statistical output on the floor and even starting in 27 games.

[1] Volkov won a gold medal at the 1988 Summer Olympics, as a member of the senior Soviet Union national basketball team.