SYNOPSIS. A critical review of past and current theories of mammalian brain evolution is presented in order to discuss conceptual problems that persist in the field. Problems with the concept of homology arise because of the interaction of cell lineages and axonal connectivity in the determination of structural features of the brain. Focusing on the continuity of information represented by ontogenetic mechanisms as opposed to morphological features avoids many of these problems and suggests homological relationships that otherwise have gone unnoticed. Many apparently progressive trends and parallelisms in mammalian brain evolution turn out to result from the influence of underlying developmental homologies. Confusions about evolutionary advancement, increasing architectonic differentiation, and the evolution of new brain structures result from a failure to appreciate how increasing brain size can bias developmental processes with respect to axonal competition, increased cellular metabolic demands and decreased information processing efficiency. Explanations of the evolution of novel structures and new connectional patterns are criticized for their failure to consider the constraints of neural developmental processes. The correlations between structural neogenesis, functional specialization and size changes in brain evolution are explained by a theory of competitive displacement of neural connections by others during development under the biasing influences of differential allometry, cell death or axon-target affinity changes. The “displacement hypothesis” is used to propose speculative accounts for the differential enlargement and multiplication of cortical areas, the origins of mammalian isocortex, the unusual features of dolphin cortex and the dramatic structural and functional reorganizations that characterize human brain evolution.