Muller had a 19-season NHL career that included winning a Stanley Cup championship with the Montreal Canadiens in 1993. But he's likely to be remembered by many as the player taken No. 2 in the 1984 NHL Draft (by the New Jersey Devils) after Mario Lemieux was selected by the Pittsburgh Penguins at No. 1.

The Devils selected Muller after he had 94 points (31 goals, 63 assists) in 49 games for Guelph of the Ontario Hockey League in 1983-84, as well as playing for Canada at the 1984 Sarajevo Olympics. He quickly became a cornerstone player in New Jersey, helping the Devils advance to the Stanley Cup Playoffs for the first time in 1987-88, his first season as captain, by scoring 37 goals and finishing with 94 points.

Muller scored 31 and 30 goals in the next two seasons. But after he dropped to 19 in 1990-91, the Devils traded him to the Montreal Canadiens on Sept. 20, 1991.

Muller quickly became a favorite in Montreal and his scoring touch also returned; he finished with 77 points (36 goals, 41 assists) in 1991-92, matched his goal, assist and point totals from 1987-88 in 1992-93 and followed that by scoring 10 goals and finishing with 17 points in 20 games to help the Canadiens win the Stanley Cup.

Muller never approached those offensive totals again. He was named captain of the Canadiens for the 1994-95 season, but was traded to the New York Islanders on April 5, 1995, beginning a stretch that saw him traded three times in less than two years. He reached the 20-goal mark for the final time in 1996-97, when he played 66 games with the Toronto Maple Leafs before being traded to the Florida Panthers.

After two more seasons with the Panthers, Muller became a free agent and signed with the Dallas Stars on Dec. 15, 1999. He made it back to the Stanley Cup Final in 2000, although the Stars lost to the Devils in six games, and played four seasons for Dallas before officially announcing his retirement on Sept. 2, 2003. Muller finished with 959 points (357 goals, 602 assists) in 1,349 NHL games, and 69 points (33 goals, 36 assists) in 127 playoff games.

Muller joined the Canadiens coaching staff as an assistant in 2006. He coached the Carolina Hurricanes from 2011-14, but they failed to make the playoffs in any of his three seasons. He rejoined the Canadiens as an associate coach in 2016.