Supercapacitors, such as electric double-layer capacitors (EDLCs) and pseudocapacitors, are becoming increasingly important in the field of electrical energy storage. Theoretical study of energy storage in EDLCs focuses on solving for the electric double-layer structure in different electrode geometries and electrolyte components, which can be achieved by molecular simulations such as classical molecular dynamics (MD), classical density functional theory (classical DFT), and Monte-Carlo (MC) methods. In recent years, combining first-principles and classical simulation to investigate the carbon-based EDLCs has become increasingly popular due to the importance of quantum capacitance in graphene-like 2D systems. More recently, the development of joint density functional theory (JDFT) enables self-consistent electronic-structure calculation for an electrode being solvated by an electrolyte. In contrast with the large amount of theoretical and computational effort on EDLCs, theoretical understanding of pseudocapacitance is very limited. In this dissertation project, we first study the carbon-based EDLCs and focus on several important aspects of EDLCs including quantum capacitance, nitrogen doping, dielectric screening, and edge effect. Then, based on our physical understanding on EDLCs, we designed novel 2D boron supercapacitors, which exhibit promising capacitive performance comparing with conventional carbon electrodes. Finally, we also introduced how to study pseudocapactive mechanism through first principle calculation with solvation model technique. Two typical pseudocapacitor systems are investigated: RuO2(110) and Ti3C2Tx (T=O,OH) in H2SO4 electrolyte. Based on our study, the relation between EDL and redox behavior were revealed. We summarize and conclude with an outlook for the future of materials design and discovery for capacitive energy storage.