In recent years, unmanned aerial vehicles (UAVs), especially small and light multicopters driven by electrical motors and batteries, have experienced a boom in applications. The electrical drive system is a central component of these UAVs. This paper introduces the basics of these drives and presents control methods for them using permanent magnet synchronous motors (PMSMs). Control of these drives is based on field-oriented control (FOC) optimised for high speed (for instance, 200 el. krpm). For the multicopter drives, sensorless control is preferred, i.e., no position or speed sensor on the motors is necessary. Therefore, in this paper, the rotor position is estimated by a sensorless method based on a back electromotive force (back emf) observer combined with a start-up process. The parametrisation methods of the observer and the start-up process are described as well. The observer and the integration of it in multicopter drives are the major innovative parts of this paper. These introduced methods are verified by simulation and experiments. In experiments two motors are considered. One is applied to operate at the maximal speed up to more than 200 el. krpm. The other is a special UAV drive motor and applied for experiments with propeller, under similar operating conditions as UAVs. The results prove the performance and effectiveness of the introduced methods.