Brother of Will Thompson, professional actor and creator of Free Native, and Luke Milstead, a two-time Texas academic All-State athlete.

While with the Marlins; Thompson was selected as organizational Pitcher of the Month, Player of the Week, and he represented his club as a member of the South Atlantic League All-Star Team.

The Washington Nationals acquired Thompson at the 2009 trade deadline in exchange for first baseman Nick Johnson.

In 2015, Thompson joined the Twins' bullpen and pitched primarily in a middle-relief role, contributing largely to the team's first-half success.

Upon the return of Ervin Santana from steroid suspension, Thompson was demoted to the Triple–A Rochester Red Wings, where he finished the season.

Thompson signed with the Sugar Land Skeeters Of The Atlantic League of Professional Baseball following his release from the Twins.