Statistics plays three important roles in brain studies. They are (1) the study of differences between brains in distinctive populations; (2) the study of the variability in the structure and functioning of the brain; and (3) the study of data reduction on large-scale brain data. I discuss these concepts using examples from past and ongoing research in brain connectivity, brain information flow, information extraction from large-scale neuroimaging data, and neural predictive modeling. Having dispensed with the past, I attempt to present a few areas where statistical science facilitates brain decoding and to write prospectively, in the light of present knowledge and in the quest for artificial intelligence, about questions that statistical and neurobiological communities could work closely together to address in the future.