Economic models generally assume agents learn according to the classical Bayesian paradigm, or else view departures from that paradigm as the result of behavioral biases or cognitive limitations. Yet when researchers in economics and statistics are themselves learning how to model something -- in particular, when they are trying to learn potentially high-dimensional models -- their approach is increasingly guided by not by a Bayesian prior but the objective of statistically robust performance: guarantees that their learning rule will select an approximately best-performing model in some class no matter the true data-generating process. This paper develops a framework for modeling statistically robust learners. First, we formalize a general notion of statistical robustness that applies to learning from potentially indirect and heterogeneous sources of information, and then extend the classical Vapnik–Chervonenkis learnability results to this setting to give a sharp characterization of when robust learning is possible. Second, we show that robust learning is fundamentally different from Bayesian learning in complex learning problems with misspecification by proving an upper bound on the robustness guarantees of Bayesian learning for any prior. Third, we apply these results to define statistically robust learning equilibrium in games, which replaces the best-fit condition of Berk-Nash equilibrium with optimal robust learning conditions. An application to an asset trading game illustrates that statistically robust equilibrium can provide more intuitively appealing predictions than modeling agents as misspecified Bayesian learners.