We present a new framework for auction design and analysis that we term "best-response auctions". We use this framework to show that the simple and myopic best-response dynamics converge to the VCG outcome and are incentive compatible in several well-studied auction environments (Generalized Second Price auctions, and auctions with unit-demand bidders). Thus, we establish that in these environments, given that all other bidders are repeatedly best-responding, the best course of action for a bidder is to also repeatedly best-respond. Our results generalize classical results in economics regarding convergence to equilibrium and incentive compatibility of ascending-price English auctions. In addition, our findings provide new game-theoretic justifications for some well-studied auction rules. Best-response auctions provide a way to bridge the gap between the full-information equilibrium concept and the usual private-information auction theory.