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The powerful methods we have for solving the atomic structure of bulk crystals fail for nanostructured materials and there are currently no broadly applicable, quantitative and robust methods to replace them. The solution of this nanostructure problem is one of the grand challenges of nanoscience. Here we give a brief overview of the various classes of nanostructured materials, and review the methods that are currently used to study their structure. We suggest that a robust solution of the nanostructure problem will involve interactions between scientists from multiple disciplines such as materials scientists, physicists, chemists, computer scientists and applied mathematicians, working within a complex modeling paradigm that combines theory and experiment in a self-consistent computational framework.