Electrochemical capacitors, also called supercapacitors, store energy in two closely spaced layers with opposing charges, and are used to power hybrid electric vehicles, portable electronic equipment and other devices. By offering fast charging and discharging rates, and the ability to sustain millions of cycles, electrochemical capacitors bridge the gap between batteries, which offer high energy densities but are slow, and conventional electrolytic capacitors, which are fast but have low energy densities. Here, we demonstrate microsupercapacitors with powers per volume that are comparable to electrolytic capacitors, capacitances that are four orders of magnitude higher, and energies per volume that are an order of magnitude higher. We also measured discharge rates of up to 200 V s(-1), which is three orders of magnitude higher than conventional supercapacitors. The microsupercapacitors are produced by the electrophoretic deposition of a several-micrometre-thick layer of nanostructured carbon onions with diameters of 6-7 nm. Integration of these nanoparticles in a microdevice with a high surface-to-volume ratio, without the use of organic binders and polymer separators, improves performance because of the ease with which ions can access the active material. Increasing the energy density and discharge rates of supercapacitors will enable them to compete with batteries and conventional electrolytic capacitors in a number of applications.