Nanostructured carbon materials, such as graphene and nanoporous carbon, have become increasingly prominent for use as electrodes in supercapacitors, owing to their high specific and volumetric surface area and good electrical conductivity. A conventional understanding of supercapacitors relates the high power to fast ion accumulation at the polarized electrode interface, forming the so-called electric double layer, and the low energy to limited electrode surface area (SA). As such, low-dimensional carbon nanostructures have been extensively explored. However, anomalous and nonlinear relationships between observed capacitances and SAs have prompted a need to revise our mechanistic understanding of charge storage. In this talk, we present our recent findings regarding charge storage mechanisms in carbon-based supercapacitors from combined quantum mechanical and classical molecular dynamics simulations. Our first-principles studies suggest that the total interfacial capacitance (C_T) of graphene-based supercapacitors is determined from both electrode (C_Q) and electric double layer (C_D) capacitances which are in series. It has also been demonstrated that the C_Q, and thereby C_T, can be significantly enhanced as a result of changes to the electronic structure through chemical functionalization, doping, and/or structural deformation. Furthermore, our voltammetric molecular dynamics simulations have revealed the complex non-equilibrium processes associated with extreme confinement of ionic liquid electrolytes within subnanometer pores. Based on these results, we will also discuss a mechanistic perspective centered around ion reorganization kinetics, particularly the dependence of ion migration efficiency, and relatedly, the capacitance, on pore morphology.