With the rapid development of artificial intelligence, big data, and the Internet of Things technologies, the fault monitoring and diagnosis techniques for elevator systems are undergoing unprecedented transformations. To promote research in the field of elevator fault monitoring and diagnosis, this paper reviews the research progress in data monitoring and processing, fault diagnosis, and state prediction of elevators at different stages of operation and maintenance. The methods for achieving these stages are classified. In response to the challenges faced by intelligent elevators in fault monitoring and diagnosis, the paper suggests that future research should focus on a deeper understanding of elevator operational mechanisms, improve the acquisition and processing of multi-source heterogeneous data, and further enhance the generalization, stability, and accuracy of fault diagnosis and prediction models. This will lay a solid foundation for the development of the elevator industry.