We show that in nanoscale two-terminal resistive switches the resistance switching can be dominated by the formation of a single conductive filament. The probabilistic filament formation process strongly affects the device operation principle, and can be programmed to facilitate new functionalities such as multibit switching with partially formed filaments. In addition, the nanoscale switches exhibit excellent performance metrics making them well suited for memory or logic operations using conventional or emerging hybrid nano/CMOS architectures.