Edge computing as a promising technology provides lower latency, more efficient transmission, and faster speed of data processing since the edge servers are closer to the user devices. Each edge server with limited resources can offload latency-sensitive and computation-intensive tasks from nearby user devices. However, edge computing faces challenges such as resource allocation, energy consumption, security and privacy issues, etc. Auction mechanisms can well characterize bidirectional interactions between edge servers and user devices under the above constraints in edge computing. As demonstrated by the existing works, auction and mechanism design approaches are outstanding on achieving optimal allocation strategy while guaranteeing mutual satisfaction among edge servers and user devices, especially for scenarios with scarce resources. In this paper, we introduce a comprehensive survey of recent researches that apply auction approaches in edge computing. Firstly, a brief overview of edge computing including three common edge computing paradigms, i.e., cloudlet, fog computing and mobile edge computing, is presented. Then, we introduce fundamentals and backgrounds of auction schemes commonly used in edge computing systems. After then, a comprehensive survey of applications of auction-based approaches applied for edge computing is provided, which is categorized by different auction approaches. Finally, several open challenges and promising research directions are discussed.