Among terrestrial mammals, elephants share the unique status, along with humans and great apes, of having large brains, being long-lived and having offspring that require long periods of dependency. Elephants have the largest brains of all terrestrial mammals, including the greatest volume of cerebral cortex. In contrast to what one might expect from such a large-brained species, the performance of elephants in cognitive feats, such as tool use, visual discrimination learning and tests of "insight" behavior, is unimpressive in comparison to the performance by chimpanzees and, of course, humans. Where elephants do seem to excel is in long-term, extensive spatial-temporal and social memory. In addition, elephants appear to be somewhat unique among non-human species in their reactions to disabled and deceased conspecifics, exhibiting behaviors that are mindful of "theory-of-mind" phenomena. Information gleaned from studies on the neural cytoarchitecture of large brains reveals that the neurons of the cerebral cortex of elephants are much less densely populated than in large-brained primates. The interactions between cortical neurons would appear to be more global and less compartmentalized into local areas, and cortical information processing slower, than in great apes and humans. Although focused neural cytoarchitecture studies on the elephant are needed, this comparative perspective on the cortical neural cytoarchitecture appears to relate to differences in behavior between elephants and their primate counterparts.