This review examines aspects of cetacean brain structure related to behaviour and evolution. Major considerations include cetacean brain-body allometry, structure of the cerebral cortex, the hippocampal formation, specialisations of the cetacean brain related to vocalisations and sleep phenomenology, paleoneurology, and brain-body allometry during cetacean evolution. These data are assimilated to demonstrate that there is no neural basis for the often-asserted high intellectual abilities of cetaceans. Despite this, the cetaceans do have volumetrically large brains. A novel hypothesis regarding the evolution of large brain size in cetaceans is put forward. It is shown that a combination of an unusually high number of glial cells and unihemispheric sleep phenomenology make the cetacean brain an efficient thermogenetic organ, which is needed to counteract heat loss to the water. It is demonstrated that water temperature is the major selection pressure driving an altered scaling of brain and body size and an increased actual brain size in cetaceans. A point in the evolutionary history of cetaceans is identified as the moment in which water temperature became a significant selection pressure in cetacean brain evolution. This occurred at the Archaeoceti - modern cetacean faunal transition. The size, structure and scaling of the cetacean brain continues to be shaped by water temperature in extant cetaceans. The alterations in cetacean brain structure, function and scaling, combined with the imperative of producing offspring that can withstand the rate of heat loss experienced in water, within the genetic confines of eutherian mammal reproductive constraints, provides an explanation for the evolution of the large size of the cetacean brain. These observations provide an alternative to the widely held belief of a correlation between brain size and intelligence in cetaceans.