Supercapacitors, or electrochemical capacitors, are a power storage system applied for harvesting energy and delivering pulses during short periods of time. The commercially available technology is based on charging an electrical double-layer (EDL), and using high surface area carbon electrodes in an organic electrolyte. This review first presents the state-of-the-art on EDL capacitors, with the objective to better understand their operating principles and to improve their performance. In particular, it is shown that capacitance might be enhanced for carbons having subnanometric pores where ions of the electrolyte are distorted and partly desolvated. Then, strategies for using environment friendly aqueous electrolytes are presented. In this case, the capacitance can be enhanced through pseudo-faradaic contributions involving i) surface functional groups on carbons, ii) hydrogen electrosorption, and iii) redox reactions at the electrode/electrolyte interface. The most promising system is based on the use of aqueous alkali sulfate as electrolyte allowing voltages as high as 2 V to be reached, due to the high overpotential for di-hydrogen evolution at the negative electrode.