This paper presents new identification results for models of first–price, second–price, ascending (English), and descending (Dutch) auctions. We consider a general specification of the latent demand and information structure, nesting both private values and common values models, and allowing correlated types as well as ex ante asymmetry. We address identification of a series of nested models and derive testable restrictions enabling discrimination between models on the basis of observed data. The simplest model—symmetric independent private values—is nonparametrically identified even if only the transaction price from each auction is observed. For richer models, identification and testable restrictions may be obtained when additional information of one or more of the following types is available: (i) the identity of the winning bidder or other bidders; (ii) one or more bids in addition to the transaction price; (iii) exogenous variation in the number of bidders; (iv) bidder–specific covariates. While many private values (PV) models are nonparametrically identified and testable with commonly available data, identification of common values (CV) models requires stringent assumptions. Nonetheless, the PV model can be tested against the CV alternative, even when neither model is identified.