Bykov started out playing for the team of his home city, Traktor Chelyabinsk in 1979.

[3][4] On 10 August 2006, Bykov was named as the new head coach of the Russian national hockey team, taking over from Vladimir Krikunov.

After losing 3–7 to Canada and finishing 6th at the 2010 Winter Olympics and failing to win gold in two subsequent WCs, he was fired by the RHF.

Salavat Yulaev Ufa named Bykov as new head coach on 14 May 2009 starting from the 2009–2010 season.

SKA Saint Petersburg appointed Bykov as new head coach on 4 April 2014.