In the era of massive data and information, electronic computer processing systems face increasingly greater demands on computing power and energy consumption. Bottlenecks such as the "memory wall" and "power wall" inherent in the traditional von Neumann architecture, coupled with the slowing down or even invalidation of Moore's Law, have posed significant challenges to electronic chips in terms of computing speed and power consumption. Utilizing optical computing as an alternative to traditional electronic computing represents one of the most promising avenues to address current challenges in computing power and power consumption. This review systematically summarized the research progress of optical neural network architectures and algorithms in both on-chip integration and free space, and described typical research efforts in detail. Then, the advantages and disadvantages of these two types of optical neural networks and the training strategies of optical neural networks were discussed and compared. Finally, the potential challenges that optical neural networks may encounter were discussed in depth, and a forward-looking perspective on their future development was offered.