in 1984 Muller started his junior career with the
Kingston Canadians of the
Ontario Hockey League, but his most successful junior seasons were with the
Guelph Platers. There was a dispute in 1984 between the Platers and the Canadian Olympic Team, who wanted Muller to play with them at the
1984 Winter Olympics. The Platers owner was upset over losing Muller for so much time, but eventually they came to an agreement and Muller played in the Olympics. He was drafted second overall by the
New Jersey Devils in the
1984 NHL entry draft behind
Mario Lemieux. Although New Jersey had a surprisingly successful run in the
1988 playoffs, they never became a serious
Stanley Cup contender while Muller was with them. After walking out of training camp on September 16, 1991, over a contract dispute, he was traded along with
Roland Melanson to the
Montreal Canadiens for
Stéphane Richer and
Tom Chorske on September 20. Muller quickly became a fan favourite in Montreal, and he helped them win the
Stanley Cup in 1993. He was traded to the
New York Islanders during the
1994–95 NHL season. Initially, he was reluctant to report to the Islanders, then played a handful of games in an uninterested manner before team management decided that his poor attitude outweighed his potential contributions on the ice and barred him from the team. Eventually, the Islanders recalled Muller, but he refused to report, freeing the Islanders from their contractual obligations to pay him. Ultimately, Muller was traded at a discount to the
Toronto Maple Leafs, in a three team trade that saw Muller and
Don Beaupre go to the Maple Leafs,
Martin Straka,
Ken Belanger and the rights to
Bryan Berard go to the Islanders while
Damian Rhodes and the rights to
Wade Redden went to the
Ottawa Senators. Muller had his last 20 goal season with the Maple Leafs the next season, but he was traded to the
Florida Panthers for prospect
Jason Podollan as the Leafs fell out of the playoff picture. Muller struggled in Florida, scoring just four goals in the whole
1998–99 NHL season. His last break came when he signed with the
Dallas Stars in the middle of the
1999–2000 season. He spent four seasons with the Stars on a line that included
Mike Keane and
John MacLean. He retired at the end of the 2002–03 season. Muller played in the
NHL All-Star Game six times (1985, 1986, 1988, 1990, 1992, 1993). ==Coaching career==