Energy storage devices are considered to be the mainstay of a thriving economy that intends to meet the sustainable development goal of providing affordable and clean energy. Technologies for electrochemical energy storage based on carbon-based nanomaterials have the potential to be the driving force behind research into the next generation of energy storage devices. Recently, supercapacitor-based energy storage devices have been embraced as one of the most promising and efficient new technologies. Because supercapacitors have poor energy density (compared to batteries and fuel cells), there is a pressing need to engineer and design novel electrode materials to enhance their electrochemical performance. In general, research into efficient electrode materials for advanced electrochemical energy storage systems is ongoing. Carbon-based nanostructures have piqued the curiosity of researchers as electrode materials for decades due to their high surface area density. Hence, this chapter discusses the role of 0D, 1D, 2D, and 3D carbon-based nanostructure materials in supercapacitor applications and their electrochemical performances. Additionally, various carbon-based nanostructured materials have been briefly discussed as supercapacitor electrode materials, including nanotubes, nanofibers, nanowires, nanorods, nanospheres, graphene, graphene oxide, and nanosheets. Finally, carbon-based nanostructure materials used in flexible supercapacitors are discussed and highlighted as attractive innovations for flexible electronics.