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In this book, we present studies on nanoscale resistance switching devices (memristive devices). The devices show excellent resistance switching properties such as fast switching time, high on/off ratio, good data retention and high endurance. As digital memory devices, the devices are ideally suited in a crossbar architecture which offers ultra-high density and intrinsic defect tolerance capability. As an example, a high-density 1kb crossbar memory was demonstrated, proving its promising aspects for memory and reconfigurable logic applications. Furthermore, we demonstrated that the devices can also exhibit controlled analog switching behavior and function as flux controlled memristors. The memristors can be used in biology-inspired neuromorphic circuits in which signal processing efficiency orders of magnitude higher than conventional digital computer systems can be reached. As a prototype illustration, we showed Spike Timing Dependent Plasticity (STDP), one of the key learning rules in biological systems, can be realized by CMOS neurons and memristor synapses.