**1. Introduction**

The increasing global energy demand due to a modern technology-dependent lifestyle puts increasing pressure on traditional nonrenewable energy resources such as fossil fuels [1, 2]. The global trend to use portable, flexible electronics and the increase in global environmental awareness push toward the use and continuous development of eco-friendly, sustainable energy conversion and storage devices [3, 4]. Supercapacitors are essential devices among energy storage devices because of their quick charging and discharging processes, high power densities, extended cycle lives, minimal maintenance requirements, long lifespans, and environmental friendliness [4]. Both the electric double layer capacitor, which stores energy by electrostatic means, and the pseudocapacitor, which keeps energy through redox reactions, are subtypes of the supercapacitor. In most cases, the hybrid electrodes can store energy in electrochemical and electrostatic methods [5]. Similar to all other devices, the performance of supercapacitors is highly dependent on the characteristics of the materials they utilize. Continuous developments of carbon materials are rapidly being employed in energy storage devices because of their advantages, including the simplicity of modifying and manipulating pore structure, surface functionality, surface area, and low cost. Furthermore, the structural integrity of the carbon framework ensures that the electrode material's cyclic stability and capacitance retention are maintained throughout time [6].

In recent years, significant progress has been made in developing carbon nanostructure composites for high-performance energy conversion and storage devices. The recent advancement of nanoscience and nanotechnology has created novel graphitic carbon nanomaterials with multi-dimensions, such as two-dimensional (2D) graphene, (1D) carbon nanotubes (CNT), and dimensionless (0D) fullerene [7]. This chapter introduces recent supercapacitor advancements based on fundamental carbon nanostructures; graphene, carbon nanotubes, and fullerene.
