A composition comprising at least one high-density graphene-based monolith, said monolith comprising a three-dimensional structure of graphene sheets crosslinked by covalent carbon bonds and having a density of at least 0.1 g/cm.sup.3. Also provided is a method comprising: preparing a reaction mixture comprising a suspension and at least one catalyst, said suspension selected from a graphene oxide (GO) suspension and a carbon nanotube suspension; curing the reaction mixture to produce a wet gel; drying the wet gel to produce a dry gel, said drying step is substantially free of supercritical drying and freeze drying; and pyrolyzing the dry gel to produce a high-density graphene-based monolith. Exceptional combinations of properties are achieved including high conductive and mechanical properties.
FEDERAL FUNDING STATEMENT
 The United States Government has rights in the invention pursuant to Contract No. DE-AC52-07NA27344 between the U.S. Department of Energy and Lawrence Livermore National Security, LLC, for the operation of Lawrence Livermore National Laboratory.