Lithium and sodium batteries with polysulfide electrolyte

A battery comprising: at least one cathode, at least one anode, at least one battery separator, and at least one electrolyte disposed in the separator, wherein the anode is a lithium metal or lithium alloy anode or an anode adapted for intercalation of lithium ion, wherein the cathode comprises material adapted for reversible lithium extraction from and insertion into the cathode, and wherein the separator comprises at least one porous, electronically conductive layer and at least one insulating layer, and wherein the electrolyte comprises at least one polysulfide anion. The battery provides for high energy density and capacity. A redox species is introduced into the electrolyte which creates a hybrid battery. Sodium metal and sodium-ion batteries also provided.