The fluoride of a fissionable material dissolved in molten fluorides of other cations can serve as the fuel of a circulating-fuel nuclear reactor. These fluorides have a slowing-down power about one-half or one-fourth of the slowing-down power of dense graphite. The resonance escape probability depends strongly on the cation but is always less than that of carbon. The consequences of these properties for various reactor applications are discussed. Techniques for critical experiments for molten fluoride reactors have been developed, and the physics aspects of operation of the ARE have been analyzed. Operation of the ARE demonstrated that molten-fluoride reactors have strong negative temperature coefficients, mainly as a result of fuel expansion. The ARE was shown to be very stable and to be a slave to the power load. No Xe135 poisoning was found in the ARE, and the radioactivity of the fuel after removal from the reactor was less than it would have been if all fission fragments had been retained. The loss of delayed neutrons by fuel circulation modified the inhour equation but not the stability of the ARE.