Several attractive applications call for the organization of memristive devices (or other resistive non-volatile memory (NVM)) into large, densely-packed crossbar arrays. While resistive-NVM devices frequently possess some degree of inherent nonlinearity (typically 3-30× contrast), the operation of large (1000×1000 device) arrays at low power tends to require quite large (1e7) ON-to-OFF ratios (between the currents passed at high and at low voltages). One path to such large nonlinearities is the inclusion of a distinct access device (AD) together with each of the state-bearing resistive-NVM elements. While such an AD need not store data, its list of requirements is almost as challenging as the specifications demanded of the memory device. Several candidate ADs have been proposed, but obtaining high performance without requiring single-crystal silicon and/or the high processing temperatures of the front-end-of-the-line- which would eliminate any opportunity for 3D stacking-has been difficult. We review our work at IBM Research-Almaden on high-performance ADs based on Cucontaining mixed-ionic-electronic conduction (MIEC) materials [1-7]. These devices require only the low processing temperatures of the back-end-of-the-line, making them highly suitable for implementing multi-layer cross-bar arrays. MIEC-based ADs offer large ON/OFF ratios (1e7), a significant voltage margin Vm (over which current <10 nA), and ultra-low leakage (< 10 pA), while also offering the high current densities needed for phase-change memory and the fully bipolar operation needed for high-performance RRAM. Scalability to critical lateral dimensions < 30 nm and thicknesses < 15 nm, tight distributions and 100% yield in large (512 kBit) arrays, long-term stability of the ultra-low leakage states, and sub-50 ns turn-ON times have all been demonstrated. Numerical modeling of these MIEC-based ADs shows that their operation depends on Cu+ mediated hole conduction. Circuit simulations reveal that while scaled MIEC devices are suitable for large crossbar arrays of resistive-NVM devices with low (< 1.2 V) switching voltages, stacking two MIEC devices can support large crossbar arrays for switching voltages up to 2.5 V.