As a graphene-like structural material, hexagonal boron nitride (h-BN) possesses many superior properties. Owing to their enhanced qualities such as simple device structure, low power consumption, and good scalability potential, h-BN memristors are receiving increasing attention and are currently considered to hold great application prospects in the fields of computing and storage, artificial neural networks, and neuromorphic computing. In this paper, a classification of memristors is introduced, the resistive switching mechanism of the h-BN memristor is discussed, and the research status of the h-BN memristor is reviewed. Finally, the current challenges of the h-BN memristor are pointed out, and the paper concludes with an outlook of the future direction of development.