Facing the explosive growth of data, a number of new micro-nano devices with simple structure, low power consumption, and size scalability have emerged in recent years, such as neuromorphic computing based on memristor. The selection of resistive switching layer materials is extremely important for fabricating of high performance memristors. As an organic-inorganic hybrid material, metal-organic frameworks (MOFs) have the advantages of both inorganic and organic materials, which makes the memristors using it as a resistive switching layer show the characteristics of fast erasing speed, outstanding cycling stability, conspicuous mechanical flexibility, good biocompatibility, etc. Herein, the recent advances of MOFs-based memristors in materials, devices, and applications are summarized, especially the potential applications of MOFs-based memristors in data storage and neuromorphic computing. There also are discussions and analyses of the challenges of the current research to provide valuable insights for the development of MOFs-based memristors.