Inspired by the structure and principles of the human brain, spike neural networks (SNNs) appear as the latest generation of artificial neural networks, attracting significant and universal attention due to their remarkable low-energy transmission by pulse and powerful capability for large-scale parallel computation. Current research on artificial neural networks gradually change from software simulation into hardware implementation. However, such a process is fraught with challenges. In particular, memristors are highly anticipated hardware candidates owing to their fast-programming speed, low power consumption, and compatibility with the complementary metal–oxide semiconductor (CMOS) technology. In this review, we start from the basic principles of SNNs, and then introduced memristor-based technologies for hardware implementation of SNNs, and further discuss the feasibility of integrating customized algorithm optimization to promote efficient and energy-saving SNN hardware systems. Finally, based on the existing memristor technology, we summarize the current problems and challenges in this field.