In the last few million years, the hominin brain more than tripled in size. Comparisons across evolutionary lineages suggest that this expansion may be part of a broader trend toward larger, more complex brains in many taxa. Efforts to understand the evolutionary forces driving brain expansion have focused on climatic, ecological, and social factors. Here, building on existing research on learning, we analytically and computationally model the predictions of two closely related hypotheses: The Cultural Brain Hypothesis and the Cumulative Cultural Brain Hypothesis. The Cultural Brain Hypothesis posits that brains have been selected for their ability to store and manage information, acquired through asocial or social learning. The model of the Cultural Brain Hypothesis reveals relationships between brain size, group size, innovation, social learning, mating structures, and the length of the juvenile period that are supported by the existing empirical literature. From this model, we derive a set of predictions-the Cumulative Cultural Brain Hypothesis-for the conditions that favor an autocatalytic take-off characteristic of human evolution. This narrow evolutionary pathway, created by cumulative cultural evolution, may help explain the rapid expansion of human brains and other aspects of our species life history and psychology.