The large size and complex organization of the human brain makes it unique among primate brains. In particular, the neocortex constitutes about 80% of the brain, and this cortex is subdivided into a large number of functionally specialized regions, the cortical areas. Such a brain mediates accomplishments and abilities unmatched by any other species. How did such a brain evolve? Answers come from comparative studies of the brains of present-day mammals and other vertebrates in conjunction with information about brain sizes and shapes from the fossil record, studies of brain development, and principles derived from studies of scaling and optimal design. Early mammals were small, with small brains, an emphasis on olfaction, and little neocortex. Neocortex was transformed from the single layer of output pyramidal neurons of the dorsal cortex of earlier ancestors to the six layers of all present-day mammals. This small cap of neocortex was divided into 20-25 cortical areas, including primary and some of the secondary sensory areas that characterize neocortex in nearly all mammals today. Early placental mammals had a corpus callosum connecting the neocortex of the two hemispheres, a primary motor area, M1, and perhaps one or more premotor areas. One line of evolution, Euarchontoglires, led to present-day primates, tree shrews, flying lemurs, rodents and rabbits. Early primates evolved from small-brained, nocturnal, insect-eating mammals with an expanded region of temporal visual cortex. These early nocturnal primates were adapted to the fine branch niche of the tropical rainforest by having an even more expanded visual system that mediated visually guided reaching and grasping of insects, small vertebrates, and fruits. Neocortex was greatly expanded, and included an array of cortical areas that characterize neocortex of all living primates. Specializations of the visual system included new visual areas that contributed to a dorsal stream of visuomotor processing in a greatly enlarged region of posterior parietal cortex and an expanded motor system and the addition of a ventral premotor area. Higher visual areas in a large temporal lobe facilitated object recognition, and frontal cortex, included granular prefrontal cortex. Auditory cortex included the primary and secondary auditory areas that characterize prosimian and anthropoid primates today. As anthropoids emerged as diurnal primates, the visual system specialized for detailed foveal vision. Other adaptations included an expansion of prefrontal cortex and insular cortex. The human and chimpanzee-bonobo lineages diverged some 6-8 million years ago with brains that were about one-third the size of modern humans. Over the last two million years, the brains of our more recent ancestors increased greatly in size, especially in the prefrontal, posterior parietal, lateral temporal, and insular regions. Specialization of the two cerebral hemispheres for related, but different functions became pronounced, and language and other impressive cognitive abilities emerg...