Lithium-ion batteries have become the mainstream energy storage solution for many applications, such as electric vehicles and smart grids. However, various faults in a lithium-ion battery system (LIBS) can potentially cause performance degradation and severe safety issues. Developing advanced fault diagnosis technologies is becoming increasingly critical for the safe operation of LIBS. This paper provides a comprehensive review of fault mechanisms, fault features, and fault diagnosis of various faults in LIBS, including internal battery faults, sensor faults, and actuator faults. Future trends in the development of fault diagnosis technologies for a safer battery system are presented and discussed.