The physical structure of white matter fiber bundles constrains their function. Any behavior that relies on transmission of signals along a particular pathway will therefore be influenced by the structural condition of that pathway. Diffusion-weighted magnetic resonance imaging provides localized measures that are sensitive to white matter microstructure. In this review, we discuss imaging evidence on the relevance of white matter microstructure to behavior. We focus in particular on motor behavior and learning in healthy individuals and in individuals who have suffered a stroke. We provide examples of ways in which imaging measures of structural brain connectivity can inform our study of motor behavior and effects of motor training in three different domains: (1) to assess network degeneration or damage with healthy aging and following stroke, (2) to identify a structural basis for individual differences in behavioral responses, and (3) to test for dynamic changes in structural connectivity with learning or recovery.