RFBs having solid hybrid electrodes can address at least the problems of active material consumption, electrode passivation, and metal electrode dendrite growth that can be characteristic of traditional batteries, especially those operating at high current densities. The RFBs each have a first half cell containing a first redox couple dissolved in a solution or contained in a suspension. The solution or suspension can flow from a reservoir to the first half cell. A second half cell contains the solid hybrid electrode, which has a first electrode connected to a second electrode, thereby resulting in an equipotential between the first and second electrodes. The first and second half cells are separated by a separator or membrane.