Overbidding in auctions has been attributed to e.g. risk aversion, loser regret, level-k, and cursedness, relying on varying identifying assumptions. I argue that "type projection'" organizes these findings and largely captures observed behavior. Type projection formally models that people tend to believe others have object values similar to their own - a robust psychological phenomenon that naturally applies to auctions. First, I show that type projection generates the main behavioral phenomena observed in auctions, including increased sense of competition ("loser regret") and broken Bayesian updating ("cursedness"). Second, re-analyzing data from seven experiments, I show that type projection explains the stylized facts of behavior across private and common value auctions. Third, in a structural analysis relaxing the identifying assumptions made in earlier studies, type projection consistently captures behavior best, in-sample and out-of-sample. The results reconcile bidding patterns across conditions and have implications for behavioral and empirical analyses as well as policy.