It is commonly assumed that functional brain connectivity reflects structural brain connectivity. The exact relationship between structure and function, however, might not be straightforward. In this review we aim to examine how our understanding of the relationship between structure and function in the 'resting' brain has advanced over the last several years. We discuss eight articles that directly compare resting-state functional connectivity with structural connectivity and three clinical case studies of patients with limited white matter connections between the cerebral hemispheres. All studies examined show largely convergent results: the strength of resting-state functional connectivity is positively correlated with structural connectivity strength. However, functional connectivity is also observed between regions where there is little or no structural connectivity, which most likely indicates functional correlations mediated by indirect structural connections (i.e. via a third region). As the methodologies for measuring structural and functional connectivity continue to improve and their complementary strengths are applied in parallel, we can expect important advances in our diagnostic and prognostic capacities in diseases like Alzheimer's, multiple sclerosis, and stroke.