If a failure in the components of a photovoltaic (PV) system, such as PV module, controller, inverter, load, cable, etc. goes undetected and uncorrected, it can seriously affect the efficiency, safety, and reliability of the entire PV power plant. In addition, fires can occur if specific faults, such as arc, ground, and line-to-line faults remain unresolved. Therefore, PV system (PVS) fault diagnoses are crucial for PV power plant reliability, efficiency, and safety. Many fault diagnosis methods and techniques for PVS components have been developed. In addition, with the development of PV devices, more advanced and intelligent diagnostic technologies are continuously being researched and developed. However, a systematic and thorough analysis, summary, and conclusion are still urgently required. Thus, this paper introduces the types, causes, and impacts of PVS faults, and reviews and discusses the methods proposed in the literature for PVS fault diagnosis, and in particular, failures in PV arrays. Special attention is paid to the optimization direction of various fault diagnosis methods under different priorities, and their limitations, feasibility, complexity, and cost-effectiveness. Finally, challenges and suggestions are put forward for future research.