A method of making a mechanically robust, electrically conductive ultralow-density carbon nanotube-based aerogel, including the steps of dispersing nanotubes in an aqueous media or other media to form a suspension, adding reactants and catalyst to the suspension to create a reaction mixture, curing the reaction mixture to form a wet gel, drying the wet gel to produce a dry gel, and pyrolyzing the dry gel to produce the mechanically robust, electrically conductive ultralow-density carbon nanotube-based aerogel. The aerogel is mechanically robust, electrically conductive, and ultralow-density, and is made of a porous carbon material having 5 to 95% by weight carbon nanotubes and 5 to 95% carbon binder.