A number of applications call for the organization of resistive non-volatile memory (NVM) into large, densely-packed crossbar arrays. While resistive-NVM devices often possess some degree of inherent nonlinearity (typically 3-30 x contrast), the operation of large (> 1000×1000 device) arrays at low power tends to require large (> le7) ON-to-OFF ratios between the currents passed at high and at low voltages. Such large nonlinearities can be implemented by including a distinct access device together with each of the state-bearing resistive-NVM elements. While such an access device need not store data, its list of requirements is almost as challenging as the specifications demanded of the memory device. We review our work on high-performance access devices based on Cu-containing Mixed-Ionic Electronic Conduction (MIEC) materials [1-7]. (This version focuses only on the MIEC-based access device itself; previously-published longer versions of this work [8-10] also include more extensive surveys of competing devices as well.) These devices require only the low processing temperatures of the Back-End-Of-the-Line (BEOL), making them highly suitable for implementing multi-layer crossbar arrays. MIEC-based access devices offer large ON/OFF ratios (>le7), a significant voltage margin Vm (over which current < 10nA), and ultra-low leakage (<10pA), while also offering the high current densities needed for PCM and the fully bipolar operation needed for high-performance RRAM. Scalability to critical dimensions (CD) <30nm and thicknesses <15nm, tight distributions and 100% yield in large (512kBit) arrays, long-term stability of the ultra-low leakage states, and sub-50ns turn-ON times have all been demonstrated. Numerical modeling of these MIEC-based access devices 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 (<1.2V) switching voltages, a compact vertical stack of two MIEC devices in series could support large crossbar arrays for switching voltages up to 2.5V.