With the rapid development of artificial intelligence, traditional electronic neural networks can no longer meet the needs of large-scale data computing, so photonic neural network has emerged. With the advantages of parallel transmission of optical signals and ultra-low energy consumption, photonic neural networks can realize the synchronous processing and high-bandwidth transmission of multi-dimensional information based on optical computing, which demonstrates great potential in improving computing efficiency. Effective training methods are crucial for improving the performance of photonic neural networks, which attracts many teams to conduct research. This study reviews the work of major research teams at home and abroad in the training of photon neural networks, elaborates on the current main training methods, and focuses on analyzing training based on pulse timing dependent plasticity, gradient based training, evolutionary algorithms, hardware perception training, hardware error correction, online learning, and Python training frameworks for photon neural networks. Finally, the principles, advantages, and limitations of each method are analyzed, and prospects for the future development trends in this field are proposed.