Under one aspect, a non-volatile nanotube switch includes a first terminal; a nanotube block including a multilayer nanotube fabric, at least a portion of which is positioned over and in contact with at least a portion of the first terminal; a second terminal, at least a portion of which is positioned over and in contact with at least a portion of the nanotube block, wherein the nanotube block is constructed and arranged to prevent direct physical and electrical contact between the first and second terminals; and control circuitry capable of applying electrical stimulus to the first and second terminals. The nanotube block can switch between a plurality of electronic states in response to a plurality of electrical stimuli applied by the control circuitry to the first and second terminals. For each different electronic state, the nanotube block provides an electrical pathway of different resistance between the first and second terminals.