This talk will focus on theory and practice of combinatorial auctions and their application to the sale of wireless spectrum licenses.   As new wireless applications emerge worldwide, the wireless industry and government regulators are looking to reallocate wireless spectrum to better match the demand. Combinatorial auctions can play an effective role in the allocation process, but important implementation and theoretical issues remain. The talk will include an overview of recent research on the use of profit sharing contracts and core projecting auctions. Based on joint work with V. Abhishek and S.R. Williams.