The current paper details our developing understanding of the evolution of large brains in mammals. In order to do this, we first define brains that we consider to be large--those that have passed the apparent 700-gram ceiling on brain mass evolution in the class Mammalia. The over-700-gram club includes certain species within the genus Homo, order Cetacea, order Proboscidea, and suborder Pinnipedia. Our analysis suggests that selection for body size appears to be the most important factor in the evolution of large brain size, but there also appear to be internal morphophysiological constraints on large brain size evolution that need to be overcome in order for brains to break the 700-gram barrier. These two aspects appear to be common themes in the evolution of large brains. This significantly diminishes the explanatory value of selection for greater cognitive capacities as a principal factor in the evolution of enlarged brain sizes above the 700-gram threshold.