We describe a scalable method for producing continuous graphene networks by tape casting surfactant-stabilized aqueous suspensions of functionalized graphene sheets. Similar to all other highly connected graphene-containing networks, the degree of overlap between the sheets controls the tapes' electrical and mechanical properties. However, unlike other graphene-containing networks, the specific surface area of the cast tapes remains high (>400 m(2).g(-1)). Exhibiting apparent densities between 0.15 and 0.51 g.cm(-3), with electrical conductivities up to 24 kS.m(-1) and tensile strengths over 10 MPa, these tapes exhibit the best combination of properties with respect to density heretofore observed for carbon-based papers, membranes, or films.