Memristor (a word created from “memory” and “resistor” ) has been claimed as the ” missing circuit element”and research on nanoscale memristor devices has gained substantial interest recently after the development of a simple device model last year. Memristors or memristive systems are two-terminal electrical switches that exhibit both hysteresis (memory) and non-linear resistance characteristics. These properties allow them to act as promising candidates for ultra-high density memory and logic applications. In this talk, I will discuss our studies on a silicon-based memristive system. As a digital memory, the device is fully compatible with CMOS processing and exhibits excellent performance in terms of scaling potential, on/off ratio, yield, speed and retention/endurance. The resistance switching can be explained by the formation of a single conductive filament and can be programmed with on-current levels. Analog resistive switching has also been studied which allows the device to act as reconfigurable interconnects or “synapses” in neuromorphic circuits to emulate brain-like functionalities.