Darling grew up in Chicago’s southern suburb of Lemont, Illinois, and as a child idolized the Chicago Blackhawks goaltender Ed Belfour. He played minor ice hockey with the AA Vikings (Orland Park), AA Huskies (then Darien, now Romeoville) and AAA Team Illinois and Chicago Young Americans. He played in the 2002 Quebec International Pee-Wee Hockey Tournament with the Chicago Young Americans. He attended Notre Dame College in Wilcox, Saskatchewan, in eighth grade and played AAA hockey for the Hounds. He attended Lemont High School.

After bouncing around for several years through various minor hockey leagues, his goaltender coach Brian Daccord said he was not permitted to play at his hockey school until he made a dedicated commitment to the gym. It was at this time, he lost nearly 40 pounds and gave up alcohol in 2011. Darling said even at the lowest point, after being cut from what might have been the worst team in organized hockey, he never forgot something his father told him about getting ahead: “It was kind of like his motto—’Saw the wood that’s in front of you.’ ”

On July 1, 2014, the Chicago Blackhawks signed Darling as a free agent to his first NHL contract on a one-year deal. Darling made his NHL debut on October 26, 2014, against the Ottawa Senators, making 32 saves in the 2–1 win. He became the first former Southern Professional Hockey League (SPHL) player to play in an NHL game. On November 1, 2014, it was announced Darling had been reassigned to the Blackhawks’ AHL affiliate, the Rockford IceHogs, following starting goaltender Corey Crawford’s recovery from an upper-body injury. However, Darling was recalled two weeks later, on November 15, 2014.

On February 22, 2015, Darling was promoted from Rockford and placed onto Chicago’s NHL roster, replacing Antti Raanta as the team’s backup goaltender, who himself was demoted to Rockford. The Blackhawks also signed a Darling to a two-year contract extension. On March 18, 2015, Darling recorded his first NHL shutout in a Blackhawks’ victory over the New York Rangers. On April 15, 2015, Darling recorded his first playoff win after replacing Crawford in net, making 42 saves, with the Blackhawks defeating the Nashville Predators 4–3 in double overtime. Darling set an NHL record in his debut for the longest relief appearance without allowing a goal (67:44), as well as the most saves in relief without allowing a goal (42). On June 15, 2015, Darling became the first Chicago-area native player to win a Stanley Cup with the Blackhawks.

On April 28, 2017, at the conclusion of the Blackhawks season in 2016–17, Darling’s rights as a pending free agent were traded to the Carolina Hurricanes in exchange for the Ottawa Senators’ original third-round pick in the 2017 NHL Entry Draft. On May 6, 2017, Darling agreed to terms with the Hurricanes on a four-year contract. His first season with Carolina was underwhelming, as he recorded a 13–21–7 record with a 3.18 goals against average (GAA).

On November 29, 2018, the Hurricanes placed Darling on waivers. At that point, he had a .892 save percentage in seven appearances for the club. He cleared the following day, and joined the Hurricanes’ AHL affiliate, the Charlotte Checkers. On February 10, 2019, Darling was granted a “personal leave of absence” from the Charlotte Checkers and the Hurricanes organization for an undetermined period of time.

Darling played for the United States in the 2018 IIHF World Championship, mainly serving as the backup to Keith Kinkaid. He recorded featured in two wins in as many games with a 2.25 GAA and a .870 save percentage. On May 20, the United States defeated Canada 4–1 to win the bronze medal.

On June 30, 2019, Darling and a 2020 sixth-round draft pick were traded to Florida Panthers in exchange for James Reimer. He was subsequently placed on unconditional waivers for the purpose of buying out the final two years of his contract.

Darling signed with Innsbruck HC of the Austrian Hockey League in November 2019. He abruptly returned to the United States in March 2020 following the onset of the coronavirus pandemic in Europe. Darling appeared in 33 contests for Innsbruck, where he posted a 3.34 GAA and .898 save percentage prior to his departure.