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With the continuous miniaturization of conventional integrated circuits, obstacles such as excessive cost, increased resistance to electronic motion, and increased energy consumption are gradually slowing down the development of electrical computing and constraining the application of deep learning. Optical neuromorphic computing presents various opportunities and challenges compared with the realm of electronics. Algorithms running on optical hardware have the potential to meet the growing computational demands of deep learning and artificial intelligence. Here, we review the development of optical neural networks and compare various research proposals. We focus on fiber-based neural networks. Finally, we describe some new research directions and challenges.