Functional brain images are rich and noisy data that can capture indirect signatures of neural activity underlying cognition in a given experimental setting. Can data mining leverage them to build models of cognition? Only if it is applied to well-posed questions, crafted to reveal cognitive mechanisms. Here we review how predictive models have been used on neuroimaging data to ask new questions, i.e., to uncover new aspects of cognitive organization. We also give a statistical learning perspective on these progresses and on the remaining gaping holes.