Made up of Compher, Kyle Connor, and Tyler Motte, the CCM Line combined for 83 goals and 107 assists during the 2015–16 season and helped Michigan to capture their first Big Ten Men's Ice Hockey Tournament.

While he was attending college, the Sabres included Compher in a trade package with the Colorado Avalanche, the team he joined after completing his career with Michigan.

After finding success in his first full NHL season during 2017–18, Compher hoped to become Colorado's second-line center in 2018–19, a plan that was delayed when he was sidelined with a concussion.

[10] On December 3, Compher was named the Big Ten Second Star of the Week after recording three goals and an assist in a two-game series against the Ohio State Buckeyes.

[15] Michigan was eliminated in the first round of the 2014 Big Ten Men's Ice Hockey Tournament in a double-overtime 2–1 Penn State victory.

[1] After defeating Wisconsin 5–1 in the opening round of the 2015 Big Ten Men's Ice Hockey Tournament, the Wolverines won 4–1 against Michigan State in the semifinals,[21] with Compher scoring what was ultimately the game-winning goal in the second period.

Compher was named to the Big Ten All-Tournament Team,[32] while the Wolverines automatically earned a bid into the 2016 NCAA Division I Men's Ice Hockey Tournament.

[33] They faced Notre Dame in the first round of the NCAA tournament, with Compher assisting on the game-winning overtime goal from Tyler Motte.

[36] Compher's collegiate hockey career ended in 2016, at which point he chose to forego his final year of NCAA eligibility to sign a three-year entry-level contract with the Avalanche.

[37] After attending the Avalanche's 2016 training camp, Compher was assigned to the San Antonio Rampage of the American Hockey League (AHL) to begin the 2016–17 season.

[39] After Jarome Iginla was traded to the Los Angeles Kings on March 1, 2017,[40] Compher was called up to the Avalanche as his replacement, part of general manager Joe Sakic's plan to give the team a younger core.

[39] Compher was one of three rookie forwards to make the Avalanche's opening night roster for the 2017–18 season, joining Tyson Jost and Alexander Kerfoot.

[45] One of several young players to be injured around the midway point of the season, Compher returned on January 17 for a game against the San Jose Sharks.

[46] Compher's first NHL multi-goal game on March 14 moved the Avalanche up from the second to the first wild card position in the Western Conference, giving them a stronger opportunity to reach the postseason.

[48] The Avalanche, meanwhile, clinched a berth in the 2018 Stanley Cup playoffs, allowing Compher to make his NHL postseason debut in their first-round series against the Nashville Predators.

[63][64] At the time that the COVID-19 pandemic forced the indefinite suspension of the 2019–20 NHL season in March, Compher was ninth for the Avalanche with 31 points, including 11 goals, in 67 games.

[69] With a number of key Avalanche players injured towards the beginning of the 2020–21 season, Compher had an opportunity to fill in for Nathan MacKinnon,[70] centering Gabriel Landeskog and Mikko Rantanen on the top line.

[74] After another scoring drought during which he had two goals in 19 games throughout April and the first half of May, Compher recorded his first NHL hat-trick on May 12 during a 6–0 shutout win over the Los Angeles Kings.

[80] In his absence, Nicolas Aubé-Kubel, who had recently been claimed from the Philadelphia Flyers on waivers, filled in for him as the right winger for Tyson Jost and Alex Newhook's line.

[85] In the 2022 Stanley Cup playoffs, Compher played a key role in the Avalanche's first second round series victory, scoring two goals in Game 6 to help clinch the win over the St. Louis Blues.

[86] In the Western Conference Finals against the Edmonton Oilers, Compher continued to distinguish himself, notably scoring the game-winning goal in Game 3 to give the Avalanche a stranglehold on the series.

[94] That same year, Compher won a gold medal with Team USA at the 2012 IIHF World U18 Championships, recording two goals and five points in six games.

[98] The following year, he was one of several Wolverines to attend the 2015 World Junior Ice Hockey Championships,[99] where he was held pointless in five games for the fifth-place United States team.

[100] All three members of Compher's "CCM Line" at Michigan were selected to represent the United States senior team at the 2016 IIHF World Championship in Russia.