A redox flow battery is described that does not include ion-exchange resin such as an expensive proton exchange membrane but rather uses immiscible catholyte and anolyte liquids in contact at a liquid-liquid interface. Solvents and electrochemically active components of the anolyte and catholyte would not cross the liquid-liquid interface between the anolyte and catholyte, but certain ions in each of the anolyte and catholyte would cross the interface during charging and discharging of the redox flow battery. Suitable chemical options are described along with system options for utilizing immiscible phases.