For fault diagnosis techniques based on set-membership estimation, due to their theoretical advantages in handling unknown but bounded uncertainties, these methods have become an important research direction for enhancing the robustness and reliability of systems. This paper systematically reviews the fault diagnosis methods based on set-membership estimation, breaking away from the traditional review paradigm of dividing by time or field. This review takes the geometric representation form of sets as the main line and classifies the existing methods into four categories: interval type, ellipsoidal type, centrally symmetric polyhedral type, and other geometric bodies. This paper elaborates in depth on the basic principles, development trends, and performance characteristics of each category of methods. The paper further comprehensively reviews the research progress of set-membership estimation in fault diagnosis around the three core links of fault detection, isolation, and estimation, and compares and analyzes the advantages and disadvantages of different geometric description strategies in terms of computational complexity, conservativeness, and engineering applicability. On this basis, this paper systematically sorts out the typical application achievements of this method in various fields and summarizes the key challenges currently faced. Finally, the paper points out several directions worthy of in-depth research in the future.