A method of making a carbon nanotube structure includes forming a plurality of carbon nanotubes and contacting the carbon nanotubes with a polymer. A solid composition is formed from the carbon nanotubes and polymer and then shaped. For example, the solid composition can be shaped into an elongated structure such as a filament, wire, rope, cable, and the like. In at least some instances, at least some, or all, of the polymer is removed from the solid composition after it is shaped.