Supercapacitors are one of the key devices for energy-storage applications. They have energy densities much higher than those of conventional capacitors and possess much better power delivery capabilities than batteries. This makes them unique devices that can outperform both batteries and conventional capacitors under special circumstances. Nanocarbons are the main electrode materials for supercapacitors. Abundant sources of nanocarbons and facile processes of modification have led to the fabrication of cheap electrodes. In this review, we focus on the capacitance performance of highly porous activated carbons and attempt to determine the role of different pores. Elaborate discussions are presented on individual contributions from micro- and mesopores and their mutual dependence. This article also presents a comparative performance report for both random and ordered porous nanocarbons. Novel carbon materials, such as carbon nanotubes and graphene, and their contributions in this context are discussed. We summarize key techniques for the functionalization of nanocarbons and their pseudocapacitive charge-storage mechanisms. Nanocarbon composites with redox-active transition-metal oxides and conducting polymers are highlighted along with their impact as electrode materials. Ideal composite structures are highlighted and an attempt is made to determine an ideal future electrode structure for capacitors with high energy and power density.