Deep neural network has been proved to be effective in solving problems in different fields such as image, natural language, and so on. At the same time, with the continuous development of mobile Internet technology, portable devices have been rapidly popularized, and users have put forward more and more demands. Therefore, how to design an efficient and high performance lightweight neural network is the key to solve the problem. In this paper, three methods of constructing lightweight neural network are described in detail, which are artificial design of lightweight neural network, compression algorithm of neural network model, and automatic neural network architecture design based on searching of neural network architecture. The characteristics of each method are summarized and analyzed briefly, and the typical algorithms of constructing lightweight neural network are introduced emphatically. Finally, the existing methods are summarized and the prospects for future development are given.