Carbon, with its variety of allotropes and forms, is the most versatile material, and virtually any combination of mechanical, optical, electrical, and chemical properties can be achieved with carbon by controlling its structure and surface chemistry. The goal of this article is to help readers appreciate the variety of carbon nanomaterials and to describe some engineering applications of the most important of these. Many different materials are needed to meet a variety of performance requirements, but they can all be built of carbon. Considering the example of supercapacitor electrodes, zero- and one-dimensional nanoparticles, such as carbon onions and nanotubes, respectively, deliver very high power because of fast ion sorption/desorption on their outer surfaces. Two-dimensional (2D) graphene offers higher charge/discharge rates than porous carbons and a high volumetric energy density. Three-dimensional porous activated, carbide-derived, and templated carbon networks, with high surface areas and porosities in the angstrom or nanometer range, can provide high energy densities if the pore size is matched with the electrolyte ion size. Finally, carbon-based nanostructures further expand the range of available nanomaterials: Recently discovered 2D transition-metal carbides (MXenes) have already grown into a family with close to 20 members in about four years and challenge graphene in some applications.