At a time when unions are courting everyone from Amazon workers to Starbucks baristas, one industry may be ripe for organizing like no other: health care.

Unionizing efforts at hospitals and other health care providers are popping up all over the country, often with successful results. More than 1,200 resident physicians at Montefiore Medical Center in Bronx, New York, prevailed in an election last spring, for instance, joining the Committee of Interns and Residents of the Service Employees International Union. And just this week, more than 1,000 health care workers at the Ohio State University’s Wexner Medical Center scored a victory, joining the International Association of Machinists and Aerospace Workers.