Optical neural network can process information in parallel by using the technology based on free-space and integrated platform. Over the last half century, the development of integrated circuits has been limited by Moore's law. We know that neural network is based on the digital computer for successive calculation, most of which cannot be made into real-time processing system. Therefore, it is necessary to develop ONN for real-time processing and device miniaturization. In this paper, we review the progress of optical neural networks. Firstly, based on the principle of artificial neural networks, we elaborate the essence of optical matrix multiplier for linear operation. Then we introduce the optical neural network achieved by free-space optical interconnection and waveguide optical interconnection. Finally we talk about the nonlinearity in optical neural networks. With the gradual maturity of nanotechnology and the rapid advancement of silicon photonic integrated circuits, the progress of integrated photonic neural network has been promoted. Therefore, the construction of optical neural network on the future integrated photonic platform has potential application value.