Memristive elements are provided that include an active region disposed between a first electrode and a second electrode. The active region includes an switching layer of a first metal oxide and a conductive layer of a second metal oxide, where a metal on of the first metal oxide differs from a metal ion of the second metal oxide. The memristive element exhibits a nonlinear current-voltage characteristic in the low resistance state based on the oxide hetero-junction between the first metal oxide and the second metal oxide. Multilayer structures that include the memristive elements also are provided.