I discuss the role of auction theory as a tool for resource allocation and provide an overview of the preliminary theoretical results that serve as building blocks for practical auction design. I review the areas where auctions have been put to practice including in financial markets, for spectrum licenses, for ad space and for allocation of drilling rights of natural resources like oil and gas. A discussion of practical settings where bidder valuations are endogenous follows and the paper ends with the extensions of the standard Generalized Second Price (GSP) model to consumer search, common values and hierarchical bidding.