In 1992 when he was 12 years old, his sister Lesley—two years older—was diagnosed with pediatric thyroid cancer, for which she had surgery to remove all of her thyroid gland (a thyroidectomy). “Something as traumatic as that has a lasting impact,” Breslow said. “It confirmed my interest [in medicine]. Being a doctor went from being a prestigious profession to something that changes people’s lives.” The experience led Breslow to take an interest in molecular biophysics and biochemistry. Later in life, Breslow formed a non-profit foundation to help children with cancer.

Breslow was born in New Haven, Connecticut, and raised in Trumbull, Connecticut. He is Jewish, and attended Hebrew school. His family attended Congregation B’nai Israel in Bridgeport, Connecticut, where he had his bar mitzvah in 1993. 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.”

In soccer, he helped lead Trumbull High to their first-ever state tournament victory. In 1997, he was named to the Fairfield County Interscholastic Athletic Conference Boys First-Team Soccer Team. He was known for having an uncanny ability to score from very difficult and wide angles, and ranks among the school’s all-time scorers. Scholastically he excelled as well, scoring 1420 on his SAT exam.

Breslow attended Trumbull High School in Trumbull, Connecticut, graduating in 1998. He was a standout in baseball and soccer, and served as team captain in both sports during his senior year.

Breslow was captain of the Yale Bulldogs baseball team in the Ivy League. 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. As a junior, he led Yale in victories (3) and ERA (2.61; 3rd in the Ivy League), striking out 66 batters in 51⅔ innings (ranking 13th in the nation in strikeouts per nine innings). He earned All-Ivy honors that season, which included a 16-strikeout performance vs. Cornell, and a one-hit shutout at Harvard. As a senior, he led the Ivy League with a 2.56 ERA.

Breslow graduated from Yale University in 2002 with a B.A. in molecular biophysics and biochemistry, and gained admission to the NYU School of Medicine, which he deferred.

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.

He was drafted in the 26th round by the Milwaukee Brewers in 2002. Breslow deferred acceptance to the New York University School of Medicine because of his “love of the game”. As of July 2017, he had deferred his acceptance to the medical school four times, as he continued to play baseball.

In 2002, Breslow ranked fifth in the Pioneer League with six wins, going 6–2 with a 1.82 ERA in 23 appearances out of the pen for the Rookie-level Ogden Raptors. He struck out 56 in 54⅓ innings, and limited the opposition to a .218 average.

In 2003, he averaged 11⅓ strikeouts per nine innings for the Single-A Beloit Snappers of the Midwest League, fanning 80 batters in 65 innings.

In 2004, Breslow played 79 games in the Brewers system, reaching the Class A California League High Desert Mavericks. The Brewers released Breslow during the 2004 season.

Breslow reached the Major Leagues in 2005, the first Yale graduate to do so since Ron Darling (1983–95). He pitched his first game for San Diego on July 23, 2005. Breslow was also one of six Ivy Leaguers on major league rosters at the beginning of the 2009 season. In 2012, Breslow and catcher Ryan Lavarnway became the first Yale grads to be Major League teammates since 1949, and the first All-Yale battery in the major leagues since 1883.

Signed by the San Diego Padres in 2005 for $1 out of a tryout camp, he 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 earned his first big league callup on July 23, 2005. He was mistaken for the team batboy during his first day with the Padres. He became the 24th Yalie to play in Major League Baseball and the first to reach the major leagues since Ron Darling. “It wasn’t until I was playing baseball in the big leagues that I thought I could play baseball in the big leagues”, he said.

Breslow then split the rest of the season between San Diego, for whom he had a 2.20 ERA in 14 games, and the Triple-A Pacific Coast League Portland Beavers. The Padres non-tendered Breslow in December 2005.

He was signed by the Red Sox, as a minor league free agent, to a minor league contract in January 2006.

In 2006, Breslow was named an International League (Triple-A) All-Star while with the Pawtucket Red Sox. In 67 innings of work for the season, he was 7–1 with a 2.69 ERA and struck out an average of 10.3 batters per nine innings. He was selected by his teammates as the PawSox Most Valuable Pitcher. 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.

In 12 innings with the Red Sox in 2006, he posted a 3.75 ERA and had 12 strikeouts.

Breslow earned a trip to the Triple-A All-Star game in July for the second straight season for the Pawtucket Red Sox. At the end of June, Breslow’s ERA was 1.55. But his final numbers for 2007 were 2–3, 4.06 ERA, 25 walks, 73 strikeouts in 68 innings. He was promoted to Boston on September 1, 2007, but did not make an appearance and was sent back to Pawtucket on September 2 to make room on the team roster for Jon Lester. 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.

On March 23, 2008, Breslow was claimed off outright waivers by the Cleveland Indians and was added to the 40-man roster. Breslow was out of minor league options, so the Indians had to keep him on their big league club out of camp, or expose him to waivers again. Breslow won the final spot on the Indians’ Opening Day roster. “He’s strong”, Cleveland manager Eric Wedge said. “I want to be able to use him two innings. He’s done that—if you look at his innings pitched the last couple of years versus appearances.”

On May 29, 2008, the Minnesota Twins claimed Breslow off waivers. In 42 games for the Twins Breslow had a 1.63 ERA, and gave up only 24 hits in 38⅔ innings. Lefties hit .183 against him, with a .232 slugging percentage, and in save situations batters batted .100 against him, with a .100 slugging percentage. He did not give up a run in his last 14 appearances.

Breslow’s aggregate 2008 ERA of 1.91 in 47 innings was ninth-best in the American League of all pitchers with at least 40 innings pitched, and second-best among AL lefty relievers. He held all batters to a .191 batting average, a .265 on-base percentage, and a .299 slugging percentage.

In 2008, Breslow started the Strike 3 Foundation, a non-profit charity that funds pediatric cancer research.

Playing for the Twins in 2009, Breslow held left-handers to a .211 batting average and right-handers to a .226 batting average, but battled control problems in 17 appearances.

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. Oakland needed bullpen help and claimed Breslow before his 72-hour waiver period expired. Had he cleared, the Twins could have sent him to Triple-A Rochester. “We were hoping to keep him”, said assistant general manager Rob Antony. “We lost a bullpen guy without trying to lose a bullpen guy”, manager Ron Gardenhire said. “I kind of got shocked when they told me.”

Searching for an experienced left-hander for their bullpen, the Oakland Athletics claimed Breslow off waivers on May 20, 2009. According to assistant general manager David Forst, the A’s had tried to acquire him on other occasions. “I’m excited about taking a look at him”, A’s Manager Bob Geren said. “He’s a left-handed guy that’s experienced. He’s had some success at this level.” He was the A’s key lefty out of the bullpen for the remainder of the season.

He was second in the AL in appearances in 2009, with 77. Batters hit only .143 against him when there were runners in scoring position. He held all batters to a .197 batting average, and a .289 on-base percentage.

Asked in 2010 whether there was a story behind his jersey number, Breslow said: “When you spend time with many organizations over 5.5 years, you don’t really care what number you get.”

He was second in the AL in appearances in 2010 for the second year in a row, appearing in 75 games (the fifth-highest single-season total in A’s history). Only 7 of 33 inherited runners (21.2%) scored against him, third-best in the AL. He held batters to a .194 batting average, and a .272 on-base percentage. Opposing batters were 0-for-11 with zero RBIs against him with the bases loaded, which were the most bases-loaded at bats against an AL pitcher with zero RBIs since the stat was tracked beginning in 1974.

Breslow was nicknamed the “smartest man in baseball” by Minneapolis Star Tribune Twins beat writer La Velle E. Neal III, and Wall Street Journal reporter Jason Turbow wrote: “Judging by his résumé, Craig Breslow is the smartest man in baseball, if not the entire world.” In 2010 the Sporting News named him the smartest athlete on their top-20 list. In 2012, Men’s Fitness named him one of the Top 10 Smartest Athletes in Professional Sports.

In 2011, he was 0–2 with a 3.79 ERA in 67 games in which he pitched 59.1 innings. He led all relief pitchers with 5 pickoffs, and led American League relievers with 7 caught stealing.

On December 9, 2011, Breslow and Trevor Cahill were traded to the Arizona Diamondbacks for Ryan Cook, Jarrod Parker, and Collin Cowgill. Since Breslow was the last arbitration-eligible player for Arizona to be under contract, he avoided arbitration and a deal was made at $1.795 million. His salary was a $395,000 increase over the 2011 season.

On July 31, 2012, he was traded to the Boston Red Sox for outfielder Scott Podsednik and relief pitcher Matt Albers. In 23 innings in 2012 for the Red Sox, he struck out 19 and had a 2.70 ERA. He held opponents to a .206 batting average, and opposing lefties to a .184 batting average.

In 40 games, and 43.1 innings, in 2013 for Arizona before being traded, he had a 2–0 record and a 2.70 ERA with 42 strikeouts, and limited opposing batters to a .233 batting average. As of the end of the 2017 season, he was the player with the most innings pitched for Arizona without ever losing. He was one of only two pitchers with a 1.000 winning percentage with Arizona who had more than one victory, with the other being Jimmie Sherfy.

In January 2013, he signed a two-year contract with the Red Sox for at least $6.25 million. He received $2.325 million in 2013, and $3.825 million in 2014. The Red Sox had a $4 million option for 2015, with a $100,000 buyout.

In the 2013 regular season, he was 5–2 with a 1.81 ERA (third among left-handed relievers in the American League), in 61 games and 59.2 innings, and held opposing batters to a .228 batting average. His 0.65 ERA the second half of the season was fourth-best among major league relievers with at least 25 innings thrown. In his last 28 appearances of the regular season, he allowed only one run.

In the 2013 American League Division Series, he pitched 3.2 scoreless innings over 3 games, notching a win and allowing two hits and one walk while striking out four, as the Red Sox defeated Tampa Bay. In the 2013 American League Championship Series, he added 3.1 scoreless innings against the Detroit Tigers, bringing his post-season total to 7 scoreless innings in 7 appearances, in which he held the opposition to a .130 batting average. Breslow wrote a blog during the 2013 post-season. During the 2013 playoffs, he pitched in 10 of 16 games, garnering a 2.45 ERA.

During the 2015 season, Breslow was 0-4 with a 4.15 ERA for Boston, striking out 46 and walking 23 in 65 innings.

Breslow and Shaffer married on November 9, 2013—ten days after he’d won the World Series with Boston. They have twin boys, Carter and Mason, born in June 2015.

Breslow signed a minor-league contract with the Miami Marlins on February 12, 2016, with a major league option. After pitching 14 innings for the Marlins, he was released on July 18, 2016, at his request.

On July 24, 2016, Breslow signed a minor league contract with an opt-out clause with the Texas Rangers. The Rangers released him on August 7, 2016.

Breslow pitched for Israel at the 2017 World Baseball Classic during the qualifying round in September 2016. During the opening game of the tournament, Breslow was credited with the win, after throwing 26 pitches over one inning, giving up 2 hits and a walk while recording 2 strikeouts. Breslow again appeared in the final game of the series throwing only 2 pitches while getting one out.

During the 2016 offseason, Breslow began experimenting with the Rapsodo Baseball system to analyze his mechanics and spin rate on his pitches. His hope was to improve the movement on his pitches and revive his career. When he began using the system in October 2016, Breslow had 9.45 inches of horizontal break on his two-seamer. By January 2017, he was able to improve and add nearly 9 additional inches of movement on the two-seamer to 1 foot, 6.35 inches. Vertical movement on the pitch also increased by about 6 inches.

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. He was added to the team’s 40-man roster on March 20, and made the team’s opening day roster at the end of the month. He earned $1.25 million in salary, and was eligible for $1 million more possible in incentives . His contract called for him to earn bonuses of $150,000 at each of seven different appearance levels: 40, 45, 50, 55, 60, 65, and 70 games. He was designated for assignment mid-season on July 24, 2017, however, after appearing in 30 games. He was released a week later.

The Cleveland Indians signed Breslow to a minor league contract and assigned him to the Class AAA Columbus Clippers on August 4, 2017, where he had an 0-0 record with a 3.86 ERA in 7 relief appearances. He was called up to the Indians on August 26, and had an 0-0 record with a 4.15 ERA in 7 relief appearances. He held left-handed-hitters to a line of .196/.294/.286 over the course of the 2017 season. On November 2, he elected to become a free agent.

In February 2017 it was announced that Breslow would be on the roster for Israel at the 2017 World Baseball Classic main tournament. He pulled out of being on the team in round one after the Twins offered him an invite to spring training, and was placed in Team Israel’s designated pitcher pool, meaning he could be added in later rounds even though he did not play for the team in rounds one or two.

On February 12, 2018, Breslow agreed to a minor league contract with the Toronto Blue Jays that included an invitation to spring training. He was released on March 24 in a procedural move, and was re-signed days later to a new contract. 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. Overall, he pitched 28.1 innings with 30 strikeouts and was 1-1 with one save and a 5.40 ERA for the Fisher Cats, the Triple-A Buffalo Bisons in the International League, and the GCL Blue Jays in the Rookie Gulf Coast League.

After the 2018 season, he ranked 4th of all active left-handed MLB pitchers in career appearances, with 576. On November 2, 2018, he elected free agency.

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. In that position he is 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.”