He has previously played in MLB for the Colorado Rockies, New York Yankees, Atlanta Braves, Chicago Cubs, Los Angeles Dodgers, Boston Red Sox, and in Nippon Professional Baseball (NPB) for the Hokkaido Nippon-Ham Fighters.

After working in a warehouse for three years, Martin began playing catch, and felt strong enough to try out for independent league baseball.

In 2004, his senior year, the Texas High School Baseball Coaches Association named Martin to its Class 5A All-State team.

Martin suffered a shoulder injury while pitching for McLennan as a sophomore, and the Rockies opted not to offer him a contract.

After graduating from McLennan, Martin signed with the Fort Worth Cats of the United League Baseball, which is independent of MLB, for the 2007 season.

Though Martin made the team out of their tryout camp, he did not pitch in a game for the Cats due to discomfort in his shoulder.

He went to work loading trucks for UPS at Dallas/Fort Worth International Airport, moving refrigerators for Lowe's, and stocking washing machines and clothes dryers in an appliance warehouse in Arlington.

Martin noticed that his shoulder felt stronger, and with encouragement from Bostick, he agreed to attempt to play professional baseball again.

Martin threw fastballs at 95 miles per hour (153 km/h) before he was pulled aside by Pete Incaviglia, the AirHogs manager, and signed to a contract.

[12] The Red Sox assigned Martin to the Greenville Drive of the Single-A South Atlantic League to begin the 2011 season.

He had a 5–3 win–loss record with a 2.25 ERA and five saves in 42 games pitched, split between Portland and the Pawtucket Red Sox of the Triple-A International League during the 2013 season.

[6] After the 2013 season, the Red Sox traded Martin, along with pitcher Franklin Morales, to the Colorado Rockies in exchange for infielder Jonathan Herrera.

[8] Martin began the 2014 season with the Colorado Springs Sky Sox of the Triple-A Pacific Coast League.

[16] Martin made his major league debut on April 26, pitching a scoreless inning against the Los Angeles Dodgers.

[23] Martin began the season with a 0–1 record and a 3.55 ERA in 12+2⁄3 innings pitched across 15 appearances, before he went on the disabled list on May 9 due to tendinitis in his right elbow.

[29] After the 2015 season, the Yankees sold the contractual rights to Martin to the Hokkaido Nippon-Ham Fighters of Nippon Professional Baseball's Pacific League for $750,000.

[45] A free agent after the 2019 season, Martin re-signed with Atlanta on a two-year contract worth $14 million on November 19.

[48] On March 17, 2022, Martin signed a one-year contract with the Chicago Cubs worth $2.5 million, with additional achievable incentives.

[52] He started the 2023 season as a member of Boston's bullpen, and spent two weeks during the second half of April on the injured list.

[53] Martin served as an effective reliever for the Red Sox, posting a 4–1 record with a 1.05 ERA in 55 appearances before being placed on the injured list on September 28 due to a viral infection.