As a type of energy storage device between traditional capacitors and batteries, the supercapacitor has the advantages of energy saving and environmental protection, high power density, fast charging and discharging speed, long cycle life, and so forth. One of the key factors affecting the performance of supercapacitor is the electrode material. Carbon materials, such as carbon nanotube, graphene, activated carbon, and carbon nanocage, are most widely concerned in the application of supercapacitors. The synergistic effect of composites can often obtain excellent results, which is one of the common strategies to increase the electrochemical performance of supercapacitors. To further improve the performance of binary composites, it is a relatively simple method to increase the components as the "bridge" between the two materials to form the ternary composites. The review mainly introduces the current research progress of supercapacitors with pure carbon nanomaterials and multistage carbon nanostructures (composites) as electrodes. The characteristics and application directions of different pure carbon nanomaterials are introduced in detail. Different ways of multilevel structure (material) composite have their own effects on the development of high-performance supercapacitors. We also highlight the recent advances related to these fields and provide our insight into high-energy supercapacitors.