Any electrolyte with sufficient ionic conductivity may be used in a fuel cell, but to avoid concentration gradients in the electrolyte, active conduction should be via an ion produced in one electrode reaction and consumed in the other. This ion must be present at high concentration in the electrolyte. In aqueous fuel cells operating on hydrogen and oxygen, the only useful electrolytes have high concentrations of either H+ or OH-, i.e., strong acids or bases. The product of the anode reaction in aqueous acids, H+, occurs as a 'carrier ion' complexed by H2O as H(H2O)n+, where n lies between 1 and 4. The corresponding cathodic product ion in bases, OH-, is itself a 'carrier ion', the reaction product of O2-(from the reduction of O2) and H2O. Phosphoric acid is not an aqueous acid, but a unique self-ionizing amphoteric system, in effect a molten acidic (H+) salt. In molten salts, H+ could be the primary conductor, e.g., in molten bisulfates. Less corrosive carbonate melts use a cathodic supply of CO2 supplied via the gas phase to give CO22- as the O2- 'carrier ion'. A similar approach may be used in aqueous carbonates. No carrier material is needed in solid oxides, which conduct directly via O2- ion. The temperature windows for different electrolytes are limited by performance at the low end and materials considerations at the high end. As a result, there are no electrolytes capable of operation between 480 and 900 K, and between 1050 and 1220 K. Development of electrolytes for these temperature ranges would be valuable.