We report the synthesis of ultra-low-density three-dimensional macroassemblies of graphene sheets that exhibit high electrical conductivities and large internal surface areas. These materials are prepared as monolithic solids from suspensions of single-layer graphene oxide in which organic sol-gel chemistry is used to cross-link the individual sheets. The resulting gels are supercritically dried and then thermally reduced to yield graphene aerogels with densities approaching 10 mg/cm(3). In contrast to methods that utilize physical cross-links between GO, this approach provides covalent carbon bonding between the graphene sheets. These graphene aerogels exhibit an improvement in bulk electrical conductivity of more than 2 orders of magnitude (similar to 1 x 10(2) S/m) compared to graphene assemblies with physical cross-links alone (similar to 5 x 10(-1) S/m). The graphene aerogels also possess large surface areas (584 m(2)/g) and pore volumes (2.96 cm(3)/g), making these materials viable candidates for use in energy storage, catalysis, and sensing applications.