Phenotypic traits are products of two processes: evolution and development. But how do these processes combine to produce integrated phenotypes? Comparative studies identify consistent patterns of covariation, or allometries, between brain and body size, and between brain components, indicating the presence of significant constraints limiting independent evolution of separate parts. These constraints are poorly understood, but in principle could be either developmental or functional. The developmental constraints hypothesis suggests that individual components (brain and body size, or individual brain components) tend to evolve together because natural selection operates on relatively simple developmental mechanisms that affect the growth of all parts in a concerted manner. The functional constraints hypothesis suggests that correlated change reflects the action of selection on distributed functional systems connecting the different sub-components, predicting more complex patterns of mosaic change at the level of the functional systems and more complex genetic and developmental mechanisms. These hypotheses are not mutually exclusive but make different predictions. We review recent genetic and neurodevelopmental evidence, concluding that functional rather than developmental constraints are the main cause of the observed patterns.