Breslow pitched for 12 seasons in Major League Baseball (MLB) for the San Diego Padres, Boston Red Sox (including as a member of the 2013 World Series championship team), Cleveland Indians, Minnesota Twins, Oakland Athletics, Arizona Diamondbacks, and Miami Marlins.

As a senior at Yale University, where he majored in molecular biophysics and biochemistry, Breslow led the Ivy League with a 2.56 earned run average.

During his MLB career, he was called the "smartest man in baseball" by reporters at the Minneapolis Star Tribune and The Wall Street Journal.

[9][10][11][12] He has fasted while pitching on Yom Kippur, and noted: "Being Jewish is more difficult in baseball ... but I try to do what I can in terms of paying attention to holidays.

[34] As a freshman in 1999, he pitched for the Middletown Giants of the New England Collegiate Baseball League; in November 2013 he was inducted into the NECBL's Hall of Fame.

[36] In 2002, Breslow was named a Jewish Sports Review College Baseball First Team All-American, along with future major leaguers Sam Fuld and Adam Greenberg.

[44][46] Signed by the San Diego Padres in 2005 for $1 out of a tryout camp, Breslow excelled, getting $1,500 after making the Double-A Southern League Mobile BayBears, allowing a .212 average in 52 innings over 40 outings while striking out 47 and walking 17 with a 2.75 ERA.

He was promoted to Boston in the second half of the season, making him the fourth Jewish player (in addition to Kevin Youkilis, Gabe Kapler, and Adam Stern) to play for the Red Sox that year.

[53] Off the field, he helped Red Sox pitcher Josh Beckett win a bet against catcher Doug Mirabelli.

Breslow calculated how many times a baseball spins when it's thrown 90 miles an hour from the pitcher's mound to home plate.

[56] Breslow was added to the postseason roster, and has a ring from winning the 2007 World Series — without pitching a game in the majors that year.

[67] The Twins figured they had a 50–50 chance of losing Breslow when they placed him on waivers in May 2009 to clear space on their 25-man roster for fellow left-hander Sean Henn.

[82] On December 9, 2011, Breslow and Trevor Cahill were traded to the Arizona Diamondbacks for Ryan Cook, Jarrod Parker, and Collin Cowgill.

[84] In 40 games and 43+1⁄3 innings in 2013 for Arizona before being traded, Breslow had a 2–0 record and a 2.70 ERA with 42 strikeouts, and limited opposing batters to a .233 batting average.

[86] On July 31, 2012, Breslow was traded to the Boston Red Sox for outfielder Scott Podsednik and relief pitcher Matt Albers.

[31] In the 2013 regular season, Breslow was 5–2 with a 1.81 ERA (third among left-handed relievers in the American League) in 61 games and 59+2⁄3 innings, and held opposing batters to a .228 batting average.

[95] In the 2013 American League Division Series, Breslow pitched 3+2⁄3 scoreless innings over three games, notching a win and allowing two hits and one walk while striking out four, as the Red Sox defeated Tampa Bay.

[99] Breslow did save one game in the 2014 season on August 25, 2014, during an extra inning victory over American League East rival Toronto.

[107] On February 8, 2017, Breslow signed a minor league contract offered by the Minnesota Twins, which he chose over nearly a dozen competing offers—some for more money.

[118] On August 4, 2017, Breslow signed a minor league contract with the Cleveland Indians and assigned him to the Class AAA Columbus Clippers.

[82] On February 12, 2018, Breslow agreed to a minor league contract with the Toronto Blue Jays that included an invitation to spring training.

[121][124] On April 2, Breslow agreed to go to the Double-A New Hampshire Fisher Cats in the Eastern League to continue working on his new sidearm delivery.

[130] During the 2016 offseason, Breslow began experimenting with the Rapsodo Baseball system to analyze his mechanics and spin rate on his pitches.

[134] During the opening game of the tournament, Breslow was credited with the win after throwing 26 pitches over one inning, giving up two hits and a walk while recording two strikeouts.

[138] In January 2019, the Chicago Cubs hired Breslow as their Director of Strategic Initiatives for Baseball Operations, joining Theo Epstein in the team's front office.

[139] In that position, he was to "help to evaluate and implement data-based processes throughout all facets of Baseball Operations" and "support the organization's pitching infrastructure in Player Development and the major leagues.

[142] On October 25, 2023, the Boston Red Sox hired Breslow as their Chief Baseball Officer, replacing Chaim Bloom.

[144] Breslow was nicknamed the "smartest man in baseball" by Minneapolis Star Tribune Twins beat writer La Velle E. Neal III, and The Wall Street Journal reporter Jason Turbow wrote: "Judging by his résumé, Craig Breslow is the smartest man in baseball, if not the entire world.

"[154] As to the impact of his intelligence on his baseball performance, Breslow admits that he analyzes video and looks for inefficiencies in the "kinematic system" of his delivery.

[163][164] The foundation donated $500,000 to the Yale-New Haven Children's Hospital to help enhance their Pediatric Bone Marrow Transplant Program.