A comprehensive understanding of animal cognition requires the integration of studies on behavior, electrophysiology, neuroanatomy, development, and genomics. Although studies of comparative cognition are receiving increasing attention from organismal biologists, most current studies focus on the comparison of behaviors and anatomical structures to understand their adaptative values. However, to understand the most potentially complex cognitive program of the human brain a greater synthesis of a multitude of disciplines is needed. In this review, we start with extensive neuroanatomic comparisons between humans and other primates. One likely specialization of the human brain is the expansion of neocortex, especially in regions for high-order cognition (e.g., prefrontal cortex). We then discuss how such an expansion can be linked to heterochrony of the brain developmental program, resulting in a greater number of neurons and enhanced computational capacity. Furthermore, alteration of gene expression in the human brain has been associated with positive selection in DNA sequences of gene regulatory regions. These results not only imply that genes associated with brain development are a major factor in the evolution of cognition, but also that high-quality whole-genome sequencing and gene manipulation techniques are needed for an integrative and functional understanding of comparative cognition in non-model organisms.