Photonic neural networks (PNNs) are proposed to balance the demands between a substantial increase in computation ability and a decrease in computing power consumption, owing to the superiorities in terms of large bandwidth, low latency, and low power consumption in optical transmission. Hence, in recent years, PNNs have become the research hotspot both in academia and industry. By utilizing photons as the physical media, the basic computing units in artificial neural network algorithms can be built and experimentally demonstrated. In further, PNNs might be adopted as a new computing architecture with high performances and be applied to solve the practical applications. In this paper, the working principle and characteristics of the core optical devices in PNNs are described, along with the system architecture and application scenario. In addition, the present challenges and future development trends of PNNs are discussed, after reviewing the research progress of PNNs at home and aboard.