Memristive devices have shown considerable promise for on-chip nonvolatile memory and computing circuits in energyefficient systems. However, this technology is limited with regard to speed, power, VDDmin, and yield due to process variation in transistors and memrisitive devices as well as the issue of read disturbance. This paper examines trends in the design of device and circuits for on-chip nonvolatile memory using memristive devices as well as the challenges faced by researchers in its further development. Several silicon-verified examples of circuitry are reviewed in this paper, including those aimed at high-speed, area-efficient, and low-voltage applications.Index Terms-Memristive device, memristor, nonvolatile memory, recent developments in resistive memory (ReRAM), resistive RAM.