Provided is a multivalent metal-ion battery comprising an anode, a cathode, a porous separator electronically separating the anode and the cathode, and an electrolyte in ionic contact with the anode and the cathode to support reversible deposition and dissolution of a multivalent metal, selected from Ni, Zn, Be, Mg, Ca, Ba, La, Ti, Ta, Zr, Nb, Mn, V, Co, Fe, Cd, Cr, Ga, In, or a combination thereof, at the anode, wherein the anode contains the multivalent metal or its alloy as an anode active material and the cathode comprises a cathode layer of an exfoliated graphite or carbon material recompressed to form an active layer that is oriented in such a manner that the active layer has a graphite edge plane in direct contact with the electrolyte and facing or contacting the separator.