A graphene-based or carbon-based aerogel is a three-dimensional (3D) solid material in which the carbon atoms are arranged in a sheet-like nanostructure. In this study, we report the synthesis of low-density polymer-modified aerogel monoliths by 3D macro-assemblies of graphene oxide sheets that exhibit significant internal surface areas (982 m2/g) and high electrical conductivity (∼0.1 to 1 × 102 S/cm). Different types of materials were prepared to obtain a single monolithic solid starting from a suspension of single-layer graphene oxide (GO) sheets, and a polymer, made from the precursors 4-carboxybenzaldehyde and polyvinyl alcohol. These materials were used to cross-link the individual sheets by covalent bonds, resulting in wet-gels that were supercritically dried and then, in some cases, thermally reduced to yield graphene aerogel composites. The average densities were approaching 15-20 mg/cm3. This approach allowed for the modulation of distance between the sheets, pore dimension, surface area, and related properties. This specific GO/Polymer ratio has suitable malleability making it a viable candidate for use in conductivity 3D printing; it also has other properties suitable for energy storage, catalysis, sensing and biosensing applications, bioelectronics, and superconductors.