Deep neural networks have continually surpassed traditional methods on a variety of computer vision tasks. Though deep neural networks are very powerful, the large number of weights consumes considerable storage and calculation time, making it hard to deploy on resource-constrained hardware platforms such as mobile system. The number of weights in deep neural networks represents the complexity to an extent, but not all the weights contribute to the performance according to recent researches. Specifically, some weights are redundant and even decrease the performance. This survey offers a systematic summarization of existing research achievements of the domestic and foreign researchers in recent years in the aspects of network pruning, network distillation, and network decomposition. Furthermore, comparisons of compression performance are provided on several public deep neural networks. Finally, a perspective of future work and challenges in this research area are discussed.