With the development of information science technology, the complexity of industrial system is increasing, and the safety of complex industrial control system is widely concerned. How to maintain complex industrial system safety has become the focus in the field of fault diagnosis and safety control. In order to ensure the safety and reliability of the industrial systems, it is necessary to detect the faults and potential safety hazards in time and reduce the impact of faults as far as possible. In recent years, a large number of literature related to fault diagnosis and safety control have emerged. In this paper, the development of fault diagnosis and safety control methods for industrial systems and their applications in engineering are summarized. The research status and trends are also analyzed, and the direction is prospected for the future. It is expected that the paper can provide some guidance and reference to engineers and researchers.