[4] In 2007, during his junior year at New Trier High School, Moore joined the United States Hockey League's (USHL) Chicago Steel for their 2007–08 season.

[7] Prior to his rookie season with the Rangers, Moore was signed to a three-year entry-level contract with the Blue Jackets on July 21, 2009.

Moore then put up impressive numbers in the playoffs, earning 16 points in 20 games as the Rangers lost to the Windsor Spitfires in the Western Conference Finals.

After 47 games with the Falcons, Moore was recalled by the Blue Jackets and made his NHL debut in a 4–3 victory over the Edmonton Oilers on February 5, 2011.

[10] During the lockout-shortened 2012–13 season, Moore was included in the NHL trade deadline day deal made by the Blue Jackets that sent Derick Brassard, Derek Dorsett, himself and a sixth-round draft pick to the New York Rangers in exchange for Marián Gáborík and prospects Blake Parlett and Steven Delisle on April 3, 2013.

[17] When reflecting on his recovery, Moore stated he worked with Devils skills coach Pertti Hasanen and "really kind of challenged myself when I was injured.

[21] Following the Bruins elimination from the 2021 Stanley Cup playoffs, Moore underwent hip arthroscopy and labral repair surgery.