Thermal rectifiers using linear nanostructures as core thermal conductors have been fabricated. A high mass density material is added preferentially to one end of the nanostructures to produce an axially non-uniform mass distribution. The resulting nanoscale system conducts heat asymmetrically with greatest heat flow in the direction of decreasing mass density. Thermal rectification has been demonstrated for linear nanostructures that are electrical insulators, such as boron nitride nanotubes, and for nanostructures that are conductive, such as carbon nanotubes.