Career
Polák was drafted in the sixth round, 180th overall, at the 2004 National Hockey League Entry Draft by the Saint Louis Blues, the organization with which he spent his entire National Hockey League career with prior to joining the Toronto Maple Leafs in 2014. Polák was drafted in the sixth round, 180th overall, in the 2004 National Hockey League Entry Draft by the Saint Louis Blues. After playing in the Western Hockey League (WHL) in the 2004-2005 season with the Kootenay Ice, he returned to his native Czechoslovakian Republic to make his professional debut with The Human Context Vítkovice of the Czechoslovakian Extraliga.
In the 2006-2007 season, Polák returned to North America and appeared in his first National Hockey League game on 9 October 2006, against the Anaheim Ducks.
After two seasons between the Blues and their affiliate, the Peoria Rivermen, Polák made the starting roster for the Blues in the 2008-2009 season. Polák scored his first National Hockey League goal in his 57th game on 20 December 2008, against the Minnesota Wild.
He finished the season with 15 points in 69 games and was re-signed by the Blues to a two-year contract on 24 July 2009. Emerging as a mainstay in the Blues defense and establishing himself as one of the Blues" top defensive-defensemen over the next two seasons, Polák was re-signed by Saint Louis to a five-year contract extension on 2 June 2011.
On 28 June 2014, Polák was traded to the Toronto Maple Leafs in exchange for defenseman Carl Gunnarsson and a 2014 fourth-round draft pick (Ville Husso).
During his first season in Toronto, Polák set a career-high in goals scored (5). On February 22, 2016, Polák was traded to the San Jose Sharks along with Nick Spaling in exchange for second-round draft picks in 2017 and 2018, as well as forward Raffi Torres.