Remarkable achievements have been witnessed in free-space quantum key distribution (QKD), which acts as an available approach to extend the transmission range of quantum communications. The feasibility of transmitting qubits through the free-space channel with the aid of moving platforms like satellites, aircraft, unmanned aerial vehicles (UAVs) has been verified. In view of the limited working time and resource consumption of the satellite-based QKD and the last-mile challenges of connecting satellite nodes with terrestrial networks, the airborne QKD is expected to provide flexible and relay links for the large-scale integrated network. This paper reviews the recent significant progress of QKD based on aircraft or UAVs, highlights their critical techniques, and prospects the future of airborne quantum communications.