Embodiments of the present invention are directed to nanoscale memristor devices that provide nonvolatile memristive switching. In one embodiment, a memristor device comprises an active region, a first electrode disposed on a first surface of the active region, and a second electrode disposed on a second surface of the active region, the second surface opposite the first surface. The first electrode is configured with a larger width than the active region in a first direction, and the second electrode is configured with a larger width than the active region in a second direction. Application of a voltage to at least one of the electrodes produces an electric field across a sub-region within the active region between the first electrode and the second electrode.