This thesis is composed of three chapters that examine topics related to collusion in English auctions. In the first chapter, we develop a fully nonparametric identification framework and a test of collusion in ascending bid auctions. Assuming efficient collusion, we show that the underlying distributions of values can be identified despite collusive behavior when there is at least one known competitive bidder. We propose a nonparametric estimation procedure for the distributions of values and a bootstrap test of the null hypothesis of competitive behavior against the alternative of collusion. In the second chapter, we adopt a copula-based approach to identification. We succeed in showing that joint distribution function of private valuations is identifiable under certain conditions. Finally, we propose a semiparametric strategy, based on Archimedean copulas, to identify and estimate the model primitives and analyze the dependence relation between bids in English auctions. One advantage this approach has is that it allows us to separate the estimation of the marginal distribution from the estimation of the joint distribution of underlying bidder values. The third chapter is an empirical study of the municipal GIC auctions, motivated by the theoretical frameworks developed in the first two chapters.