He had a career major league ERA of 5.03 over eight seasons, including time spent with the Anaheim Angels, Chicago White Sox, Detroit Tigers, Milwaukee Brewers, Tampa Bay Devil Rays/Rays and Toronto Blue Jays, who selected Glover in the 15th round of the 1994 Major League Baseball draft.

Toward the end of the 1998 season Toronto had promoted Glover to the Double-A Knoxville Smokies but he immediately struggled, losing five games without registering a single win and seeing his ERA skyrocket to 6.75.

In 1999 however Glover pitched to an 8–2 record with Knoxville and made the Southern League All-Star team before being promoted mid-season to the Triple-A Syracuse SkyChiefs.

[4] Called up at the end of the season Glover made his major league debut with the Blue Jays on September 30, 1999, throwing one inning of no-hit shutout ball amid a 9–2 loss to the Cleveland Indians.

[2] Glover did not join the Blue Jays for the 2000 season, spending the year at Knoxville where he put together a strong winning streak but overall went 9–9 with a 5.02 ERA.

[5] On November 7, 2000 Toronto traded Glover to the Chicago White Sox for left-handed relief pitcher Scott Eyre.

"[7] Glover opened the 2001 and got off to a strong start; retiring the first sixteen hitters he faced and picking up his first major league victory on April 11 in relief of Jim Parque against Cleveland.

[8] After a rocky May Chicago demoted Glover to the Triple-A Charlotte Knights, but he returned to the team in mid-June after posting a 1.88 ERA in six starts.

[9] On July 27 Glover made his first career major league start in place of the just-traded James Baldwin; like his debut and first win, it came against the Cleveland Indians.

Exercising an option in his contract Glover was released from the Cubs and signed with the Rochester Red Wings, the Triple-A affiliate of the Minnesota Twins.

[23] In his final start of the year Glover pitched seven shutout innings in a 2–0 victory over the Cincinnati Reds, striking out a career-high ten.

Glover did not find the transition to Japanese baseball difficult and was full of praise for his new team: "I realize the Giants are a great organization, and I feel fortunate to be playing for Yomiuri."

"[26] At the end of the season Glover returned to the United States and signed a minor league contract with the Tampa Bay Devil Rays.

Glover signed with Tampa Bay for several reasons: he wanted to return to the United States, it was close to his off-season home of Lutz, Florida, and after a year in Japan he believed he was ready to break into the big leagues for good.

In a notable appearance July 30 against the Boston Red Sox he recorded the final seven outs on fifty pitches to complete a 5–2 win.

[31] Glover made his debut for the Tigers on August 18, 2008 in relief of Kenny Rogers against the Texas Rangers; he pitched a 1-2-3 inning and struck out a batter.