A reversible resistance-switching metal-insulator-metal (MIM) stack is provided which can be set to a low resistance state with a first polarity signal and reset to a higher resistance state with a second polarity signal. The first polarity signal is opposite in polarity than the second polarity signal. In one approach, the MIM stack includes a carbon-based reversible resistivity switching material such as a carbon nanotube material. The MIM stack can further include one or more additional reversible resistivity switching materials such as metal oxide above and/or below the carbon-based reversible resistivity switching material. In another approach, a metal oxide layer is between separate layers of carbon-based reversible resistivity switching material.