Comparative analysis of the behavior of modern primates, in conjunction with an accurate phylogenetic tree of relatedness, has the power to chart the early history of human cognitive evolution. Adaptive cognitive changes along this path occurred, it is believed, in response to various forms of complexity; to some extent, theories that relate particular challenges to cognitive adaptations can also be tested against comparative data on primate ecology and behavior. This paper explains the procedures by which data are employed, and uses the best currently available evidence to derive a proposal for some of the stages through which human cognition evolved, before the last common ancestor with a nonhuman, and the reasons that cognitive adaptations were favored in primate evolution.