A supercapacitor electrode comprising a solid graphene foam impregnated with a liquid or gel electrolyte, wherein the solid graphene foam is composed of multiple pores and pore walls, wherein pore walls contain a pristine graphene material having essentially zero % of non-carbon elements, or a non-pristine graphene material having 0.001% to 5% by weight of non-carbon elements wherein non-pristine graphene is selected from graphene oxide, reduced graphene oxide, graphene fluoride, graphene chloride, graphene bromide, graphene iodide, hydrogenated graphene, nitrogenated graphene, chemically functionalized graphene, or a combination thereof, and the solid graphene foam, when measured in a dried state without electrolyte, has a physical density from 0.01 to 1.7 g/cm3, a specific surface area from 50 to 3,200 m2/g, a thermal conductivity of at least 200 W/mK per unit of specific gravity, and/or an electrical conductivity no less than 2,000 S/cm per unit of specific gravity.