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In emerging artificial intelligence applications, massive matrix operations require high computing speed and energy efficiency. Optical computing can realize high-speed parallel information processing with ultra-low energy consumption on photonic integrated platforms or in free space, which can well meet these domain-specific demands. In this review, we firstly introduce the principles of photonic matrix computing implemented by three mainstream schemes, and then review the research progress of optical neural networks (ONNs) based on photonic matrix computing. In addition, we discuss the advantages of optical computing architectures over electronic processors as well as current challenges of optical computing and highlight some promising prospects for the future development.