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We report studies on nanoscale Si-based memristive devices for memory and neuromorphic applications. The devices are based on ion motion inside an insulating a-Si matrix. Digital devices show excellent performance metrics including scalability, speed, ON/OFF ratio, endurance and retention. High density non-volatile memory arrays based on a crossbar structure have been fabricated and tested. Devices inside a 1kb array can be individually addressed with excellent reproducibility and reliability. By adjusting the device and material structures, nanoscale analog memristor devices have also been demonstrated. The analog memristor devices exhibit incremental conductance changes that are controlled by the charge flown through the device. The performances of the digital and analog devices are thought to be determined by the formation of a dominant conducting filament and the continuous motion of a uniform conduction front, respectively.