Under one aspect, a method of making a nanotube switch includes: providing a substrate having a first conductive terminal; depositing a multilayer nanotube fabric over the first conductive terminal; and depositing a second conductive terminal over the multilayer nanotube fabric, the nanotube fabric having a thickness, density, and composition selected to prevent direct physical and electrical contact between the first and second conductive terminals. In some embodiments, the first and second conductive terminals and the multilayer nanotube fabric are lithographically patterned so as to each have substantially the same lateral dimensions, e.g., to each have a substantially circular or rectangular lateral shape. In some embodiments, the multilayer nanotube fabric has a thickness from 10 nm to 200 nm, e.g., 10 nm to 50 nm. The structure may include an addressable diode provided under the first conductive terminal or deposited over the second terminal.