Topology control is one of the most fundamental problems in wireless sensor networks. It is of great importance for prolonging network lifetime, reducing radio interference, increasing the efficiency of MAC (media access control) protocols and routing protocols, among other things. This paper makes a full-scale introduction to the advancement of research on topology control. Firstly, the topology control problem and the design objectives are clearly presented. Secondly, an introduction is made to representative research efforts, along with analyses and comparisons, in two aspects, power control and sleep scheduling, respectively. At the same time, the defects of those efforts are clearly pointed out. Finally, existing problems, open issues and research trends are analyzed and summarized.