Electrical bistability existing in biochemical networks is critical for the proper functionalization of living systems. The development of artificial materials with electrical bistability begun to attract much interest due to their broad application prospects, especially in the field of memristors. Metal-organic frameworks (MOFs) have advantages in regular pores, crystallinity, structural designability and easy functionalization, which can promote the construction of novel MOF-based memristors and facilitate a better understanding of switching mechanisms. Here, we highlight recent advances in electrically bistable MOFs as memristors, and discuss their switching mechanisms, including interfacial reaction, proton-transfer mechanism, metal ion migration, charge trapping/detrapping and other mechanisms. Challenges and future perspectives are also presented.