Artificial neural networks are widely used in artificial intelligence applications such as voice assistant, image recognition and natural language processing. With the rise of complexity of the application, the computational complexity has also increased dramatically. The traditional general-purpose processor is limited by the memory bandwidth and energy consumption when dealing with the complex neural network. People began to improve the architecture of the general-purpose processors to support the efficient processing of the neural network. In addition, the development of special-purpose accelerators becomes another way to accelerate processing of neural network. Compared with the general-purpose processor, it has lower energy consumption and higher performance. The article aims to introduce the designs from current general-purpose processors and special-purpose accelerators for supporting the neural network. It also summarizes the latest design innovation and breakthrough of the neural network acceleration platforms. In particular, the article provides an overview of the neural network and discusses the improvements made by various general-purpose chips to support neural networks, which include supporting low-precision operations and adding a calculation module to speed up neural network processing. Then from the viewpoint of the computational structure and storage structure, the article summarizes the customized designs of special-purpose accelerators, and describes the dataflow used by the neural network chips based on the reuse of various types of the data in the neural network. Through analyzing the advantages and disadvantages of these solutions, the article puts forward the future design trend and challenge of the neural network accelerator.