Research on fault detection (FD) and condition monitoring (CM) of rotating electrical generators for modern wind turbines has addressed a wide variety of technologies. Among these, permanent magnet synchronous generators (PMSGs) and the analysis of their electromagnetic signatures in the presence of faults deserve emphasis in this paper. PMSGs are prominent in the offshore wind industry, and methods for FD and CM of PMSGs based on electromagnetic measurements are extensively discussed in academia. This paper is a concise review of FD and CM in wind turbines and PMSGs. Terminology and fundamentals of PMSG’s operation are introduced first, aiming to offer an easy read and good reference to a broad audience of engineers and data scientists. Experience and research challenges with stator winding failures are also discussed.