Because of powerful computational capabilities, neural network technologies have taken center stage in supporting artificial intelligence’s deep learning. Neural networks aren’t the best application for conventional synaptic devices like SRAM and DRAM, though. Due to their non-volatile nature, fast performance, and scalability, memristor devices have become more and more popular as alternatives. In light of the current state of memristor technology and useful methodologies ranging from ANNs to SNNs. The use of memory resistors in different neural networks is introduced. Memristors are used in the manufacture in neuromorphic processing units for computing weighted in ANNs. Memristor-based CNNs offer advantages such as reduced power consumption and improved performance compared to traditional digital implementations. There are also advantages in applying the memristors to SNNs, including improving efficiency and reducing costs. This study explores the theory, advantages and uses of memristor devices in neural networks. This article also points out the direction to be studied in this field in future.