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The structure and behavior of the electrical double-layer capacitor (EDLC) are described. The use of activated carbon electrodes is discussed and the limitations on voltage and accessible surface area are presented. Metrics for evaluating EDLC performance are defined and previously reported results of experimental carbon nanotube (CNT) electrodes are tabulated. New experimental results of electrodes constructed of vertically aligned CNTs grown on a conducting substrate are presented. By extrapolating prior and new experimental data the energy density of CNT-based EDLCs is shown to be potentially up to seven times that of commercial activated carbon-based EDLCs.