How do large drones communicate with ATC? For large drones like the Reaper, X-47, and aircraft like that, how do the "pilots" communicate with ATC when they need to?
They have an onboard VHF radio that can be used to receive and transmit on local frequencies.

For example, on the MQ-1B Predator you will see a small fin on the back of the aircraft behind the GPS dome. That is an omni-directional antenna which can transmit VHF. The Global Hawk has a similar capability.