Online auction is an active research area with wide applications. Firstly, we analyze Nash equilibrium based auction theory and main types of common auctions. The several types of online auctions are discussed. Then, we survey the research situations of the reverse auction for online centralized procurements of government and large enterprise groups, personal article auction in public C2C auction websites, keyword auction of online search engines and double auction of grid resources. We introduce the research progress of optimal auction mechanism design, reputation evaluation of auction websites, recognition of ill-mannered behaviors in auction and customer behavior analysis for online auction. Finally, several problems for further study on online auction are presented. They include other description methods of non-probabilistic theory of auction models, mechanism design of reverse auction, position auction of online search engine with consideration of public interest, and experiment analysis of customer behaviors in auctions. http://www.sjae.org/paperInfo.aspx?ID=1179
