In this article, we highlight three questions: (1) Does human cognition rely on structured internal representations? (2) How should theories, models and data relate? (3) In what ways might embodiment, action and dynamics matter for understanding the mind and the brain? The first question concerns a fundamental assumption of most researchers who theorize about the brain. Do neural systems exploit classical compositional and systematic representations, distributed representations, or no representations at all? The question is not easily answered. Connectionism, for example, has been criticised for both holding and challenging representational views. The second quesútion concerns the crucial methodological issue of how results emerging from the various brain sciences can help to constrain cognitive scientific models. Finally, the third question focuses attention on a major challenge to contemporary cognitive science: the challenge of understanding the mind as a controller of embodied and environmentally embedded action.