The permanent magnet synchronous motor (PMSM) can be a suitable candidate for electrified propulsion in aviation. Despite the very high efficiency, heat dissipation during operation leads to performance limitations. Elevated temperatures in the electrical insulations and the magnets pose a potential safety risk that must be reduced by selective cooling. A comprehensive review is conducted to capture current research interests in cooling methods in PMSM. Cooling methods are described according to their heat transfer mechanism, grouped, and assigned to the components within the motor. Key findings of the literature reviewed are described in the context of PMSM cooling. Information on cooling media and potential combinations of cooling methods...