Emerging complex functional materials often have atomic order limited to the nanoscale. Examples include nanoparticles, species encapsulated in mesoporous hosts, and bulk crystals with intrinsic nanoscale order. The powerful methods that we have for solving the atomic structure of bulk crystals fail for such materials. Currently, no broadly applicable, quantitative, and robust methods exist to replace crystallography at the nanoscale. We provide an overview of various classes of nanostructured materials and review the methods that are currently used to study their structure. We suggest that successful solutions to these nanostructure problems will involve interactions among researchers from materials science, physics, chemistry, computer science, and applied mathematics, working within a "complex modeling" paradigm that combines theory and experiment in a self-consistent computational framework.