Gudas is a rugged, hard-hitting defenseman who is counted on to kill penalties and close out victories, but he also knows how and when to move the puck. He has evolved into a solid two-way defender who often helps his team create scoring chances.

A native of Prague, Czech Republic, Gudas is the son of Leo Gudas, who played professionally in Europe, was an Olympian in 1992 and was drafted by the Calgary Flames in 1990. Radko Gudas was selected by the Tampa Bay Lightning in the third round (No. 66) in the 2010 NHL Draft and, like his father, played in the Olympics, representing the Czech Republic in 2014.

Gudas made his NHL debut with the Lightning on March 12, 2013, against the Florida Panthers, and, in typical fashion, blocked three shots and had two hits. He was seventh among NHL rookies with 87 hits that season despite playing only 22 games.

Gudas broke out in 2013-14, his first full NHL season. He was third among Tampa Bay defensemen with 22 points (three goals) in 73 games, leading the Lightning in hits (273, tied for third in the League) and ranking second on the team in blocked shots (138). He also finished sixth in the NHL in penalty minutes (152).

Gudas began the following season with the Lightning but was traded to the Philadelphia Flyers with a first-round and third-round draft pick in 2015 for Braydon Coburn on March 2, 2015. In 2015-16, his first full season in Philadelphia, Gudas had 14 points (five goals) and was second in the NHL in hits (304).