[1] He came from an athletic family: his father Greg swam and played water polo, his mother Donna is a retired gymnast who went on to coach for Cal State Northridge, and his older brother Ted was a decathlete for the Notre Dame Fighting Irish.

[3] Glasnow attended William S. Hart High School in Santa Clarita, the alma mater of other Major League Baseball (MLB) pitchers James Shields, Trevor Bauer, and Mike Montgomery.

In late July, the Pirates promoted Glasnow to the Indianapolis Indians of the Class AAA International League.

[28] During spring training in 2018, the Pirates decided that Glasnow would start the 2018 season as a relief pitcher[29] and he appeared in 34 games with a 4.34 ERA in 56 innings.

[22] On July 31, 2018, Glasnow was traded to the Tampa Bay Rays, along with Austin Meadows and a player to be named later (Shane Baz) for Chris Archer.

[31] In his 11 starts with Tampa Bay, Glasnow posted an earned run average of 4.20, recording 64 strikeouts in 55+2⁄3 innings.

[22] After starting the 2019 season 5–0 with a 1.75 earned run average, Glasnow was named the American League Pitcher of the Month for April.

[22] In the postseason, Glasnow started the clinching game in both the Wild Card round (Blue Jays)[37] and Division Series (Yankees).

This was the second straight year Glasnow started the fifth game of the ALDS for the Rays; both times he faced off against his former teammate Gerrit Cole.

[22] However on June 15 he was diagnosed with partial tears in the ulnar collateral ligament and a flexor strain of his right elbow, which he blamed on him adjusting his routine as a result of recent MLB rule changes.

[43] On September 28, he was activated off the injured list made his 2022 season debut against the Cleveland Guardians that night, pitching three innings with three strikeouts while allowing one earned run.

[22] He also started the first game of the Wild Card Series against the Texas Rangers, taking the loss while allowing three earned runs in five innings.

[48] On December 16, 2023, the Rays traded Glasnow and Manuel Margot to the Los Angeles Dodgers in exchange for Ryan Pepiot and Jonny DeLuca.

Additionally, Glasnow agreed to a five-year contract extension for $136.5 million, which also included both club and player options for the 2028 season.

[49][50] Glasnow was selected to start for the Dodgers in the MLB Seoul Series opener against the San Diego Padres in South Korea.