A model that describes bilayered bipolar resistive random access memory (BL-ReRAM) switching in oxide with a large band gap is presented. It is shown that, owing to the large energy barrier between the electrode and thin oxide layer, the electronic conduction is dominated by trap-assisted tunneling. The model is composed of an atomic oxygen vacancy migration model and an electronic tunneling conduction model. We also show experimentally observed three-resistance-level switching in Ru/ZrO2/TaOx BL-ReRAM that can be explained by the two types of traps, i. e., shallow and deep traps in ZrO2. (c) 2015 AIP Publishing LLC.