He has previously played for the Buffalo Sabres, Winnipeg Jets, New Jersey Devils, Edmonton Oilers, Minnesota Wild, Anaheim Ducks and the Pittsburgh Penguins.

Kulikov began his career in his homeland Russia with Lokomotiv-2 Yaroslavl in the Pervaya Liga, and left his club in November 2008 to sign for the Drummondville Voltigeurs of the Quebec Major Junior Hockey League (QMJHL) in North America.

[2] Despite his age, Kulikov managed to play in 68 games with Florida in his rookie season, 2009–10, displaying high levels of skill and confidence.

With the Devils out of playoff contention, Kulikov was dealt at the trade deadline to the Edmonton Oilers in exchange for a conditional fourth-round selection in 2022 on 12 April 2021.

[10] On 3 March 2023, the Ducks traded Kulikov to the Pittsburgh Penguins in exchange for Brock McGinn and a third-round pick in the 2024 NHL Entry Draft.