Brain science and brain-like research have become the strategic frontier of international competition. The rapid development of artifical intelligence and deep learning has put forward an urgent demand for the computing capacities. In the traditional von Neumann architecture, the physical separation between memory and computing units results in power consumption wall and memory wall problems. Besides, Moore's law is gradually slowing down. Photonic neuromorphic computing, which fully combines the characteristics of high-speed optical communication, optical interconnection, optical integration, silicon-based optoelectronics and neuromorphic computing, has the advantages of ultra-high speed, large bandwidth and multi-dimension. It has wide application prospects in the fields of high-performance computing and artificial intelligence. Furthermore, it is a highly competitive solution that breaks through the limits of traditional microelectronics computing in the post-Moore era. This article reviews the work of the main research teams at home and abroad on the theory, algorithms, and devices of photonic neurons, synapses, and neural networks, and puts forward a prospect.