Autonomous delivery drone networks are coming to the US in earnest. UPS and Matternet are launching a drone "airline" that will use the robotic aircraft to carry medical samples between WakeMed's health care facilities in Raleigh, North Carolina. The drone of choice (an M2 quadcopter) can only carry up to 5lbs at distances as long as 12.5 miles, but it should still be faster, cheaper and more consistent than the current system of driving samples across town using cars. They won't have to deal with traffic snarls, after all.
This isn't the flexible drone delivery service you might have imagined. Drones will fly along fixed routes, with a trained Remote Pilot-in-Command keeping watch over the trip. It's part of the FAA's larger pilot program testing public-private partnerships involving drones, and involves the help of the FAA as well as North Carolina's Department of Transportation.
It's a modest start, but it should expand over time. UPS and Matternet both plan to use the Raleigh network to see how drones can be used at other medical facilities around the US. If this goes smoothly, you could easily see other hospitals using drones on a regular basis.