He has previously played in Major League Baseball (MLB) for the Philadelphia Phillies, Houston Astros, Toronto Blue Jays, and Seattle Mariners.

Exposed to baseball at an early age, Giles played the game while attending Rio Grande High School in Albuquerque, New Mexico.

One of the team's few bright spots that season, Giles finished fourth in National League Rookie of the Year voting.

[2] Giles attended Rio Grande High School in Albuquerque, New Mexico, where he played baseball, although he was mainly an outfielder, and used his arm strength to throw out runners rather than pitch.

[citation needed] At Yavapai, the alma mater of Curt Schilling, Giles began pitching regularly, and realized his talent on the mound.

[5] He opened the 2012 season with the Low-A Lakewood BlueClaws, and after finding success there – he recorded five saves and a 3.61 ERA, working mostly as a reliever (although occasionally as a starter)[1] – he earned a promotion to the Class A-Advanced Clearwater Threshers, with whom he worked solely out of the bullpen, and posted a 3.07 ERA and .183 batting average against (BAA).

[7] During the season, he strained each oblique, limiting him to 24 appearances in which he was 2–2 with a 6.31 ERA,[5] and perhaps hurting his control on the mound, as his walk rate ballooned to 6.7 every nine innings, in comparison to 5.5 the preceding year.

[6][7] As observers expected, Giles began the 2014 season with the Reading Phillies after spending some time with the major league club during spring training.

"[14] On June 7, 2014, Giles was promoted to the major leagues after the Phillies placed Mike Adams on the disabled list (DL).

[21] Giles ranked among the best relievers in the major leagues in many key statistical categories relating to strikeouts, ERA, and walks plus hits per innings pitched (WHIP).

[24] Coming off a "meteoric rise through the Phillies' organization last season en route to becoming one of the top young relievers in baseball", Giles opened the 2015 Philadelphia Phillies season firmly implanted as the team's setup man, with his goal of being the team's closer something he did not take for granted, noting he had to "earn that position.

[27] When the Phillies traded Jonathan Papelbon to the Washington Nationals on July 28, Giles became the team's regular closer; in his first outing as such, he recorded a save against the Toronto Blue Jays.

The Astros demoted him to the Fresno Grizzlies of the Class AAA Pacific Coast League on July 11, where in 5.1 innings he gave up 9 hits and had an 8.44 ERA.

[32] On July 30, 2018, the Astros traded Giles, Héctor Pérez, and David Paulino to the Toronto Blue Jays for Roberto Osuna.

[34] Giles successfully converted 34 consecutive save opportunities in a streak that began on September 12, 2017, when he was still a member of the Astros, and ended on April 11, 2019, in a game against the Boston Red Sox.

[34] With the 2020 Toronto Blue Jays, Giles appeared in four games, with 9.82 ERA and four hits, four walks, and six strikeouts in 3+2⁄3 innings pitched.

[47][48][49] After one start with the rookie-level Arizona Complex League Giants, Giles made three appearances for the Triple-A Sacramento River Cats, logging a 3.38 ERA with two strikeouts in 2+2⁄3 innings of work.

[54] A power pitcher, Giles' fastball has hit as high as 103 miles per hour (166 km/h), and he relies on it in tandem with a slider in which he spent much of his developmental phase building confidence.

[6] A slight decline in fastball velocity, at the beginning of the 2015 season, helped him develop more command, something he called a "blessing in disguise.