Abstract: Using virtual backbone in wireless sensor network can effectively save energy, reduce interference, and prolong lifetime, which has a wide application in the field of geometric routing and topology control. Virtual backbone can be modeled as a connected dominating set (CDS) in a graph. This paper introduces the state of art of approximation algorithms on CDS and its variations. The focus is put on theoretical results and methods. The purpose is to provide a reference for researchers who are interested in this field.