The memristor is an electronic device and the only fundamental circuit element that can directly implement memory and logic computation between electronic devices. The main characteristic of the memristor is that its resistance value varies with the direction and magnitude of the current flowing through it, and this variation is reversible. It can store charge, similar to RAM in traditional computers, but with more energy-efficient, faster, and higher-density storage. Therefore, the memristor is attracting attention in the research of artificial intelligence and neural networks. This paper summarizes the mathematical principles and application scenarios of memristive systems, including ideal memristors. two theoretically mature resistance change mechanisms are summarized, namely the con-ductive filament model (mainly for RRAM, Resistive random-access Finally, the design of memristor-related circuit components and the current state of research in artificial intelli-gence, especially in the field of neural networks, are reviewed. The authors are optimistic about the future development of memristors for medium and low power edge computing platforms and believe that memristors will become one of the computing platforms for ar-tificial intelligence.