A memory device having a memory portion connected in series with a threshold device between. The memory portion stores at least one bit of data based on at least two resistance states. The threshold device is configured to switch from a high resistance state to a low resistance state upon application of a voltage and, when the voltage is removed, to re-assume the high resistance state. Additionally, the threshold device can be configured to switch in response to both negative and positive applied voltages across the first and second electrodes. Memory elements having a memory portion and threshold device between first and second electrodes and methods for forming the memory elements are also provided.