Abstract: With the growing deployment of wireless communication technologies, radio spectrum is becoming a scarce resource. The current static spectrum management leads to low spectrum utilization in the spatial and temporal dimensions. Auction mechanism is believed to be an effective method among the most effective tools to solve or relieve the problem of radio spectrum shortage. However, designing a practical spectrum auction mechanism has to consider five major challenges: strategic behaviors of rational users, channel heterogeneity, channel spatial reusability, preference diversity and social welfare maximization. In this paper, we give a though literature survey about spectrum auction mechanism design, and point out the disadvantage of the existing works. We also present our recent work in heterogeneous spectrum management. We model the problem of heterogeneous spectrum allocation as a combinatorial auction. By jointly considering the five design challenges, we propose an efficient channel allocation mechanism and a price calculation scheme. We also prove that the proposed mechanism satisfies the strategy-proofness, and achieves approximately efficient social welfare.