The aircraft power supply system is the power source of all electrical equipment on board, thus its safety and reliability are pretty important. Against the backdrop of environmental protection and high-efficiency development needs, research and application of more/all electric aircraft technology with electric power as the core is advanced. The widespread use of electric drive devices and power electronic devices has led to the complexity of aircraft power supply system structure, which puts forward higher requirements for aircraft reliability, safety, testability and maintainability, so that researches on fault diagnosis technology for aircraft power supply systems are of great significance. This paper firstly introduced the composition structure and respective functions of aircraft power supply system. Secondly, the development process of aircraft power supply system was outlined. Thirdly, the characteristics of typical domestic and foreign power supply systems were compared. Fourthly, the main failure modes, fault characteristics and failure causes of aircraft power supply system were summarized, and a design architecture of aircraft power health management system was proposed. Fifthly, the research progress of fault diagnosis methods based on model and data were reviewed, then, the characteristics of various diagnostic methods were evaluated from aspects such as accuracy, data demand, applicability and implementation difficulty. Finally, this paper gave the challenges and development trends of fault diagnosis technology for aircraft power supply system.