Density peaks clustering (DPC) algorithm is an emerging algorithm in density-based clustering analysis which draws a decision-graph based on the calculation of local-density and relative-distance to obtain the cluster centers fast. DPC is known as only one input parameter without prior knowledge and no iteration. Since DPC was introduced in 2014, it has attracted great interests and developments in recent years. This survey first analyzes the theory of DPC and the satisfactory behaviors of DPC by comparing it with classical clustering algorithms. Secondly, DPC survey is described in terms of clustering accuracy and computational complexity, including local-density optimization, allocation-strategy optimization, multi-density peaks optimization, and computational complexity optimization, to provide a clear organization. The main representative algorithms of each category are presented simultaneously. Finally, it introduces the related application research of DPC in different fields. This overview offers a comprehensive analysis for the advantages and disadvantages of DPC, and gives a comprehensive description for the improvements and applications of DPC. It is also attempted to find out some further challenges to promote DPC research.