From Deep Blue to AlphaGo, artificial intelligence and machine learning are booming, and neural networks have become the hot research direction. However, due to the size limit of complementary metal–oxide–semiconductor (CMOS) transistors, von Neumann‐based computing systems are facing multiple challenges (such as memory walls). As the number of transistors required by the neural network increases, the development of neural networks based on the von Neumann computer is limited by volume and energy consumption. As the fourth basic circuit element, memristor shines in the field of neuromorphic computing. The new computer architecture based on memristor is widely considered as a substitute for the von Neumann architecture and has great potential to deal with the neural network and big data era challenge. This article reviews existing materials and structures of memristors, neurophysiological simulations based on memristors, and applications of memristor‐based neural networks. The feasibility and advancement of implementing neural networks using memristors are discussed, the difficulties that need to be overcome at this stage are put forward, and their development prospects and challenges faced are also discussed.