We provide efficient methods for learning strategic agents' underlying bid and value distributions by observing only the outcomes of their repeated interaction in a variety of standard auction models. In particular, given a finite set of observations---each only comprising the identity of the winner and the price they paid---in a sequence of auctions involving the same set of ex ante asymmetric bidders with independent private values, we provide algorithms for non-parametrically estimating the bid distribution of each bidder to within Wasserstein, Kolmogorov, or total variation distance on the effective support of these distributions. We provide convergence bounds for the attained distance in terms of the number of observations, number of bidders, and other relevant parameters of the problem, which are uniform in that they do not depend on the bid distributions being estimated. For first-price auctions (where bid distributions and equilibrium value distributions do not coincide) we also show provide finite-sample estimation results for agents' value distributions at Bayes-Nash equilibrium. Our estimation guarantees advance a body of work at the intersection of machine learning and econometrics with partial sample observability wherein only identification results have been previously obtained in our setting.