Under the current situation of the rapid development of brain-like artificial intelligence and the increasingly complex electromagnetic environment, the most bionic and anti-interference spiking neural network has shown great potential in computing speed, real-time information processing, and spatiotemporal data processing. Spiking neural network is the core part of brain-like artificial intelligence, which realizes brain-like computing by simulating the structure of biological neural network and the way of information transmission. This article first summarizes the advantages and disadvantages of the five models, and analyzes the characteristics of several network topologies. Then, it summarizes the spiking neural network algorithms. The unsupervised learning based on spike timing dependent plasticity (STDP) rules and four types of supervised learning algorithms are analyzed. Finally, the research on brain-like neuromorphic chips at home and abroad are reviewed. This paper aims to provide learning ideas and research directions for new colleagues in the field of spiking neural network.