The battery system, as the core energy storage device of new energy vehicles, faces increasing safety issues and threats. An accurate and robust fault diagnosis technique is crucial to guarantee the safe, reliable, and robust operation of lithium-ion batteries. However, in battery systems, various faults are difficult to diagnose and isolate due to their similar features and internal coupling relationships. In this paper, the current research of advanced battery system fault diagnosis technology is reviewed. Firstly, the existing types of battery faults are introduced in detail, where cell faults include progressive and sudden faults, and system faults include a sensor, management system, and connection component faults. Then, the fault mechanisms are described, including overcharge, overdischarge, overheat, overcool, large rate charge and discharge, and inconsistency. The existing fault diagnosis methods are divided into four main types. The current research and development of model-based, data-driven, knowledge-based, and statistical analysis-based methods for fault diagnosis are summarized. Finally, the future development trend of battery fault diagnosis technology is prospected. This paper provides a comprehensive insight into the fault and defect diagnosis of lithium-ion batteries for electric vehicles, aiming to promote the further development of new energy vehicles.