Memristor, short for memory resistor, is a type of electronic device whose resistance can be modified by the magnitude and direction of the current flowing through it. It was first theorized by Leon Chua in 1971, but it was only in 2008 that HP Labs announced that they had successfully built a working memristor.
The realization of a memristor involves the creation of a thin layer of material that exhibits resistance that can be modified based on the direction and magnitude of current passing through it. The material used for memristor fabrication must have certain properties, including a nonlinear relationship between voltage and current, as well as a mechanism for preserving the resistance state even in the absence of current.
Typical Resistive Switching Materials are Hafnium and Aluminum Oxide, as well as other metal oxides (e.g. Zirconium Oxide, Tantalum Oxide), some 2D materials (Graphene, h-BN), Perovskite Materials (e.g. BiFeO3), as well as TMDs and polymers. The material to be used depends on the target application, e.g. using polymers yields flexible, low-cost devices with low endurance while using MOS stacks yields CMOS-compatible devices with intrinsic memory capabilities, albeit rather inflexible.
A review on the switching materials of memristors is conducted in https://www.nature.com/articles/s41578-019-0159-3 while some fabricated devices and applications can be seen in the following articles:
Article Memristor crossbar array for binarized neural networks