Progress of silicon-based technology is nearing its physical limit, as the minimum feature size of components is reaching a mere 10 nm. The resistive switching behavior of transition metal oxides and the associated memristor device is emerging as a competitive technology for next-generation electronics. Significant progress has already been made in the past decade, and devices are beginning to hit the market; however, this progress has mainly been the result of empirical trial and error. Hence, gaining theoretical insight is of the essence. In the present work, we report the striking result of a connection between the resistive switching and shock-wave formation, a classic topic of nonlinear dynamics. We argue that the profile of oxygen vacancies that migrate during the commutation forms a shock wave that propagates through a highly resistive region of the device. We validate the scenario by means of model simulations and experiments in a manganese-oxide-based memristor device, and we extend our theory to the case of binary oxides. The shock-wave scenario brings unprecedented physical insight and enables us to rationalize the process of oxygen-vacancy-driven resistive change with direct implications for a key technological aspect-the commutation speed. DOI: 10.1103/PhysRevX.6.011028 Subject Areas: Condensed Matter Physics, Materials Science, Nonlinear DynamicsThe information age we live in is made possible by a physical underlayer of electronic hardware, which originates in condensed-matter physics research. Despite the great progress made in recent decades, the demand for faster and power-efficient devices continues to grow. Thus, there is urgent need to identify novel materials and physical mechanisms for future electronic-device applications. In this context, transition metal oxides (TMOs) are attracting much attention for nonvolatile memory applications [1]. In particular, TMO are associated with the phenomenon of resistive switching (RS) [2] and the memristor device [3], which is emerging as a competitive technology for nextgeneration electronics [1,[4][5][6][7][8][9][10]. The RS effect is a large, rapid, nonvolatile, reversible change of the resistance, which may be used to encode logic information. In the simplest case, one may associate high and low resistance values to binary states, but multibit memory cells are also possible [11,12].Typical systems where RS is observed are two-terminal capacitor-like devices, where the dielectric might be a TMO and the electrodes are ordinary metals. The phenomenon occurs in a strikingly large variety of systemsranging from simple binary compounds, such as NiO, TiO 2 , ZnO, Ta 2 O 5 , HfO 2 , and CuO, to more complex perovskite structures, such as superconducting cuprates and colossal magnetoresistive manganites [2,4,6,9,13].From a conceptual point of view, the main challenges for a nonvolatile memory are as follows: (i) to change its resistance within nano seconds (required for modern electronics applications), (ii) to be able to retain the state for years (i.e., n...