Analysis methods in cognitive neuroscience have not always matched the richness of fMRI data. Early methods focused on estimating neural activity within individual voxels or regions, averaged over trials or blocks and modeled separately in each participant. This approach mostly neglected the distributed nature of neural representations over voxels, the continuous dynamics of neural activity during tasks, the statistical benefits of performing joint inference over multiple participants and the value of using predictive models to constrain analysis. Several recent exploratory and theory-driven methods have begun to pursue these opportunities. These methods highlight the importance of computational techniques in fMRI analysis, especially machine learning, algorithmic optimization and parallel computing. Adoption of these techniques is enabling a new generation of experiments and analyses that could transform our understanding of some of the most complex-and distinctly human-signals in the brain: acts of cognition such as thoughts, intentions and memories.