A scanning transmission electron microscopy investigation of two nanoporous carbon materials, wood-based ultramicroporous carbon and poly(furfuryl alcohol)-derived carbon, is reported. Atomic-resolution images demonstrate they comprise isotropic, three-dimensional networks of wrinkled one-atom-thick graphene sheets. In each graphene plane, nonhexagonal defects are frequently observed as connected five- and seven-atom rings. Atomic-level modeling shows that these topological defects induce localized rippling of graphene sheets, which interferes with their graphitic stacking and induces nanopores that lead to enhanced adsorption of H2 molecules. The poly(furfuryl alcohol)-derived carbon contains larger regions of stacked layers, and shows significantly smaller surface area and pore volume than the ultramicroporous carbon.