[2] In January 2010, Allen was traded to the Drummondville Voltigeurs following the annual World Juniors tournament,[3] and posted a record of 18 wins and three losses with a .933 save percentage and 1.75 goals against average (GAA).

[4] He made his NHL debut during the 2012 Stanley Cup playoffs, coming in to briefly relieve Brian Elliott late in the Blues' second game against the Los Angeles Kings in the Western Conference semifinals on April 30.

[5] Amidst the lockout-shortened 2012–13 season, Allen was recalled to the Blues and recorded his first NHL start and win in a 4–3 overtime victory over the Detroit Red Wings on February 13, 2013.

[6] On April 17, 2014, Allen was named the Aldege "Baz" Bastien Memorial Award winner as the American Hockey League's (AHL) best goaltender for the 2013–14 season.

[7] On March 26, 2016, Allen registered a 4–0 shutout win over the Washington Capitals to help the Blues break their franchise record for longest stretch without allowing a goal.

During the 2016–17 season, Allen was pulled four times in six starts during a rough stretch of play, including a poor showing on January 19, 2017, where he allowed four goals on 10 shots against the Washington Capitals.

[18] For his efforts, Allen received recognition as the team's annual recipient of the Jacques Beauchamp Molson Trophy, awarded to the player deemed to have had a dominant role during the course of the regular season.

"[26] With Price ruled out of the lineup for the entirety of the 2022–23 season,[27] Allen, entering the final year of his contract with the Canadiens, assumed the role as the team's starting goaltender.

[28] On September 28, 2022, newly appointed team general manager Kent Hughes confirmed that he was hoping to negotiate a contract extension with Allen.

[33] Montreal began the 2023–24 season with three goaltenders on their active roster as, in addition to Allen and Montembeault, prospect Cayden Primeau was no longer exempt from waivers and thus could not be sent down to AHL affiliate Laval Rocket without possibly being lost to another team.

[41] Allen was chosen to play for the Canadian under-18 team in the 2008 World U18 Championships where he won gold and was named both top goaltender and the tournament's most valuable player (MVP).