Because auctions are among the market institutions most convincingly captured by the kind of game theoretic analysis that dominates modern economic theory, auction data provide important opportunities to evaluate modeling approaches and assess the importance in practice of strategic behavior predicted by theory. Auctions also play an increasingly important role in the allocation of public resources, so goals of efficient allocation and revenue generation provide strong policy motivations for understanding auctions. This project consists of four components that contribute to this understanding through empirical studies of auction markets and development of new statistical tools for analysis of auctions. The first component addresses estimation of demand at auctions in which sellers use reserve prices. By exploiting variation in the reserve prices that results from heterogeneity in seller valuations, one can consistently estimate the full distribution characterizing demand at standard auctions---the model primitive needed for a wide range of policy simulations. This is done without parametric distributional assumptions.The second component addresses inference from bids at English auctions in which bidders may be asymmetric or have correlated valuations. This allows also environments in which bidders, but not the econometrician, observe a common factor shifting their private values---a common situation in applications. The third component develops nonparametric tests for common values at first-price auctions. Exploiting recent advancements in the econometrics of auctions, we show how one can use variation in the number of bidders to test for the presence of the winner's curse and, therefore, common values. The fourth and final project studies an online auction market with many buyers and sellers trading a homogeneous object. It addresses the effects of auction rules, seller reputation and other auction characteristics on bidder participation and bids. Arbitrage behavior is documented, and the prevalence and predictors of fraudulent seller behavior are studied.