Disclosed here is a composition comprising at least one graphene aerogel comprising a three-dimensional structure of graphene sheets, wherein the graphene sheets are covalently interconnected, and wherein the graphene aerogel is highly crystalline. Also described is a method for making a graphene aerogel, comprising preparing a mixture comprising a graphene oxide suspension and at least one catalyst; curing the reaction mixture to produce a wet gel; drying the wet gel to produce a dry gel; and pyrolyzing the dry gel at a temperature of 1500-3500° C. to produce the graphene aerogel.