We introduce a new framework for understanding how cognitive systems (e.g., humans) learn from experience, based on the concept of representational capacity—the relative amount of representational resources devoted to encoding past experiences. Most paradigms in cognitive science have operated under the assumption that these resources are constrained, forcing cognitive systems to compress rich and noisy experiences to effectively generalize to new situations. We leverage recent advances in computer science to outline the implications of learning with excess capacity, or applying even more representational resources than needed to perfectly memorize all the details of one’s past experiences. In particular, we review evidence suggesting that excess capacity systems can exhibit many of the characteristics of human learning, such as the simultaneous ability to memorize individual experiences and generalize knowledge to new situations. We define and differentiate between constrained (not enough), sufficient (just enough), and excess (more than enough to perfectly capture all the details of one’s past experiences) capacity. We derive empirical properties of learning in each of these capacity regimes, and compare these predictions to effects documented for human learning. We highlight the broad implications of this framework for advancing theoretical and empirical work across cognitive, clinical, and developmental psychology.