Mesostructured composite materials, with features ranging from 20 to 500 A in size, are obtained by the kinetically controlled competitive assembly of organic and inorganic species into nanostructured domains. Short-range order is limited, and long-range order is determined by weak forces such as van der Waals or hydrogen-bonding. Three-dimensional mesoporous materials obtained by removing the organic phase are of particular interest for applications such as catalysis and chemical sensing or separation, for which structural features such as cavity shape, connectivity and ordered bimodal porosity are critical. But atomic-scale structural characterization by the usual diffraction techniques is challenging for these partially ordered materials because of the difficulty in obtaining large (> 10 microm) single crystals, and because large repeat spacings cause diffraction intensities to fall off rapidly with scattering angle so that only limited small-angle data are available. Here we present a general approach for the direct determination of three-dimensional mesoporous structures by electron microscopy. The structure solutions are obtained uniquely without pre-assumed models or parametrization. We report high-resolution details of cage and pore structures of periodically ordered mesoporous materials, which reveal a highly ordered dual micro- and mesoscale pore structure.