With the development of green aviation and the continuous progress of new energy technology, electric aircraft have also been developed rapidly. As the core of electric aircraft, the electric propulsion system is also achieving more and more attention. Permanent magnet synchronous motor (PMSM) has become an ideal solution for electric propulsion system of electric aircraft due to its high power density and high efficiency. As its independent of position sensor, the sensorless control technology of PMSM can better satisfy the requirement of high reliability under the high altitude and complex environment of electric aircraft. Firstly, the main methods of sensorless control of PMSM for electric propulsion system of electric aircraft is summarized and compared. Secondly, the key technologies and difficulties of sensorless control of PMSM are analyzed, including rotor starting position detection, low-speed startup, and medium and high-speed operation. Finally, the problems existing in the current research are summarized, and the future development is prospected.