Fault detection and diagnosis (FDD) is of utmost importance in ensuring the safety and reliability of electric vehicles (EVs). The EV’s power train and energy storage, namely the electric motor drive and battery system, are critical components that are susceptible to different types of faults. Failure to detect and address these faults in a timely manner can lead to EV malfunctions and potentially catastrophic accidents. In the realm of EV applications, Permanent Magnet Synchronous Motors (PMSMs) and lithium-ion battery packs have garnered significant attention. Consequently, fault detection methods for PMSMs and their drives, as well as for lithium-ion battery packs, have become a prominent area of research. An effective FDD approach must possess qualities such as accuracy, speed, sensitivity, and cost-effectiveness. Traditional FDD techniques include model-based and signal-based methods. However, data-driven approaches, including machine learning-based methods, have recently gained traction due to their promising capabilities in fault detection. This paper aims to provide a comprehensive overview of potential faults in EV motor drives and battery systems, while also reviewing the latest state-of-the-art research in EV fault detection. The information presented herein can serve as a valuable reference for future endeavors in this field.