Simpson (elbow) threw a 20-pitch bullpen session July 9, MLB.com reports.
Simpson opened the season on the injured list after being diagnosed with left elbow neuritis, but he appeared to be tracking toward a brief stay on the shelf. However, after making a rehab appearance April 6, Simpson incurred a setback and ultimately underwent surgery later that month. Nearly three months later, Simpson is finally starting to make some real progress in the recovery process as he conducts his rehab at the Marlins' facility in Jupiter, Fla. He could be cleared to start facing hitters in live batting practice shortly after the All-Star break.