Recently, stemming from the rapid development of artificial intelligence, which has gained expansive success in pattern recognition, robotics, and bioinformatics, neuroscience is also gaining tremendous progress. A kind of spiking neural network with biological interpretability is gradually receiving wide attention, and this kind of neural network is also regarded as one of the directions toward general artificial intelligence. This review introduces the following sections, the biological background of spiking neurons and the theoretical basis, different neuronal models, the connectivity of neural circuits, the mainstream neural network learning mechanisms and network architectures, etc. This review hopes to attract different researchers and advance the development of brain-inspired intelligence and artificial intelligence.