Smyly attended the University of Arkansas, where he played college baseball for the Arkansas Razorbacks baseball team in the Southeastern Conference (SEC) of the National Collegiate Athletic Association (NCAA) Division I. In 2008 he did not play, as he had a fractured left elbow into which two screws were inserted. As a redshirt freshman in 2009, Smyly came within two outs of pitching the first no-hitter at the NCAA Division I championship tournament in 18 years.

During the summer following his 2009 season, Smyly pitched for the Duluth Huskies of the Northwoods League where he played for a brief time under former New York Mets Manager Terry Collins. Serving in the Razorbacks starting rotation in 2010, Smyly was 9-1 with a 2.80 ERA and 114 strikeouts in 103 innings, and was named All-SEC.

The Detroit Tigers drafted Smyly in the second round (68th overall) of the 2010 MLB draft. He signed with the Tigers, receiving a $1.1 million signing bonus. Pitching for the Lakeland Tigers of the Class A-Advanced Florida State League and the Erie SeaWolves of the Class AA Eastern League, Smyly was named the Tigers Minor League Pitcher of the Year in 2011, pitching to an 11–6 win–loss record in 22 games (21 starts) with a 2.07 earned run average (ERA) and 130 strikeouts in 126 innings pitched. He was also FSL Pitcher of the Week on June 13, and an MiLB.com Tigers Organization All-Star.

After the 2011 season, Smyly pitched for the United States national baseball team in the 2011 Baseball World Cup and the 2011 Pan American Games, winning the silver medal. Smyly also pitched for Team USA in the 2017 World Baseball Classic.

Heading into the 2012 season, MLB.com ranked Smyly the 82nd-best prospect in baseball, while Baseball America ranked him the third-best prospect in the Tigers organization, behind Jacob Turner and Nick Castellanos. The Tigers invited Smyly to spring training in 2012, allowing him to compete for a spot in the Tigers starting rotation. Smyly won the competition, beginning the 2012 season in the starting rotation of the Detroit Tigers, though he made one start with the Toledo Mud Hens of the Class-AAA International League on April 7 prior to being called up for his MLB debut on April 12. On June 14, he was placed on the disabled list (retroactive to June 11) due to a blister on his left hand. Following the Tigers trade deadline acquisition of starter Aníbal Sánchez from the Miami Marlins, Smyly spent much of August and September coming out of the Tigers bullpen.

On July 31, 2014, the Detroit Tigers traded Smyly to the Tampa Bay Rays, along with Willy Adames, in a three-team deal that also sent Austin Jackson to the Seattle Mariners, Nick Franklin from the Mariners to the Rays, and David Price to the Tigers. On September 9, Rays’ manager Joe Maddon announced they would shut down Smyly for the remainder of the season, after he had pitched a career-high 153 innings. After being traded to the Rays, Smyly went 3–1 with a 1.70 ERA in seven starts. Opponents hit .155 against him, a figure that led the AL over that span. For the 2014 season he was 9–10 with a 3.24 ERA in 28 games, 25 of which were starts.

In 2015 he was 5–2 with a 3.11 ERA in 12 starts, as he struck out 77 batters in 66⁄3 innings.

On February 4, 2016, Smyly won his arbitration case against the Rays. He earned $3.75 million in 2016. In 2016 he was 7–12 with a 4.88 ERA in 30 starts in which he pitched 175⁄3 innings. The 32 home runs he gave up were fifth-most in the American League.

On January 11, 2017, the Rays traded Smyly to the Seattle Mariners for Mallex Smith, Ryan Yarbrough, and Carlos Vargas. Smyly began the season on the disabled list. On June 28, the team announced Smyly would need Tommy John surgery for a torn left elbow ulnar collateral ligament, which he had the following month, ending his season with Seattle without him having started a game.

On December 12, 2017, Smyly signed a two-year, $10 million deal with the Chicago Cubs. During the 2018 season, after recovering from his surgery Smyly made a single appearance in the minor leagues, pitching one inning for the Class A South Bend Cubs, striking out three.

On November 2, 2018, the Cubs traded Smyly and a player to be named later to the Texas Rangers in exchange for a player to be named later. He was placed on the disabled list on April 20 with a left arm injury. On June 20, he was designated for assignment. On June 25, he was released by Texas. For the portion of the 2019 season that he pitched for Texas, he was 1–5 with an 8.42 ERA in 13 games, 9 of which were starts, as he struck out 52 batters in 51⁄3 innings.

On July 1, 2019, Smyly signed a minor league deal with the Milwaukee Brewers. Starting three games for the AAA San Antonio Missions, he was 1–0 with a 4.97 ERA with 18 strikeouts in 12 ⁄3 innings. He elected free agency on July 18.

On July 21, 2019, Smyly signed a major league contract with the Philadelphia Phillies. With the Phillies he was 3-2 with a 4.45 ERA, as in 12 starts, he pitched 62 ⁄3 innings and struck out 68 batters; the 32 home runs he gave up for the season between Texas and Philadelphia were the 10th-most in the major leagues.

In 2020，his four-seam averaged nearly 94mph, at 2249 rpm while his curveball also increased to 80 mph average at 2153 rpm compared to 1950 rpm in 2019. The improvements were due to his longer arm swing, higher glove position off the raised front thigh at windup, and a faster arm speed at release, but also having well-recovered from Tommy John surgery.

On January 16, 2020, Smyly signed a one-year deal with the San Francisco Giants.