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Supercapacitors are an innovative and promising technology in the field of energy storage. In the present study, we use modeling via computer simulation as a technique to study the dynamic processes of charging and discharging. This methodology is complementary to experiments. Various model systems composed of different structures of carbon electrodes, in contact with either pure or solvated ionic liquid, polarized at positive or negative potentials were investigated. From the data obtained, we identify several characteristic times for the charging mechanism of supercapacitors. Furthermore, we determine the influence of the structure of the electrode material, and the effects of potential and solvation on dynamical processes. [ABSTRACT FROM AUTHOR]