Because of their advantages of high energy and power density, low self-discharge rate, and long lifespan, lithium-ion batteries (LIBs) have been widely used in many applications such as electric vehicles, energy storage systems, smart grids, etc. However, lithium-ion battery systems (LIBSs) frequently malfunction because of complex working conditions, harsh operating environment, battery inconsistency, and inherent defects in battery cells. Thus, safety of LIBSs has become a prominent problem and has attracted wide attention. Therefore, efficient and accurate fault diagnosis for LIBs is very important. This paper provides a comprehensive review of the latest research progress in fault diagnosis for LIBs. First, the types of battery faults are comprehensively introduced and the characteristics of each fault are analyzed. Then, the fault diagnosis methods are systematically elaborated, including model-based, data processing-based, machine learning-based and knowledge-based methods. The latest research is discussed and existing issues and challenges are presented, while future developments are also prospected. The aim is to promote further researches into efficient and advanced fault diagnosis methods for more reliable and safer LIBs.