He is currently an assistant coach for the Laval Rocket of the American Hockey League.
He was known for playing in the style of an agitator and for his ascension to the NHL from being an undrafted player in the ECHL.
After a two-year career in the Quebec Major Junior Hockey League (QMJHL), he played in the minor leagues for three seasons.
He was signed by the Vancouver Canucks in 2005 from their American Hockey League (AHL) affiliate, the Manitoba Moose.
Burrows established himself as a checking forward with the Canucks in his first three NHL seasons before emerging as a scorer with four consecutive 25-plus-goal seasons from 2008–09 to 2011–12.
Before making it to the NHL, Burrows also enjoyed a prolific ball hockey career, competing in national and international tournaments in the summers.
In 2005, he was named the International Ball Hockey Player of the Year.
He has also been inducted into the Canadian and International Ball Hockey Hall of Fame.