With recent progress in material science, resistive random access memory (RRAM) devices have attracted interest for nonvolatile, low-power, nondestructive readout, and high-density memories. Relevant performance parameters of RRAM devices include operating voltage, operation speed, resistance ratio, endurance, retention time, device yield, and multilevel storage. Numerous resistive-switching mechanisms, such as conductive filament, space-charge-limited conduction, trap charging and discharging, Schottky Emission, and Pool-Frenkel emission, have been proposed to explain the resistive switching of RRAM devices. In addition to a discussion of these mechanisms, the effects of electrode materials, doped oxide materials, and different configuration devices on the resistive-switching characteristics in nonvolatile memory applications, are reviewed. Finally, suggestions for future research, as well as the challenges awaiting RRAM devices, are given.