Despite decades of research, some of the most basic issues concerning the extraordinarily complex brains and behavior of birds and mammals, such as the factors responsible for the diversity of brain size and composition, are still unclear. This is partly due to a number of conceptual and methodological issues. Determining species and group differences in brain composition requires accounting for the presence of taxon-cerebrotypes and the use of precise statistical methods. The role of allometry in determining brain variables should be revised. In particular, bird and mammalian brains appear to have evolved in response to a variety of selective pressures influencing both brain size and composition. "Brain" and "cognition" are indeed meta-variables, made up of the variables that are ecologically relevant and evolutionarily selected. External indicators of species differences in cognition and behavior are limited by the complexity of these differences. Indeed, behavioral differences between species and individuals are caused by cognitive and affective components. Although intra-species variability forms the basis of species evolution, some of the mechanisms underlying individual differences in brain and behavior appear to differ from those between species. While many issues have persisted over the years because of a lack of appropriate data or methods to test them; several fallacies, particularly those related to the human brain, reflect scientists' preconceptions. The theoretical framework on the evolution of brain, cognition, and behavior in birds and mammals should be reconsidered with these biases in mind.