Thermally conductive polymer composites offer new possibilities for replacing metal parts in several applications, including power electronics, electric motors and generators, heat exchangers, etc., thanks to the polymer advantages such as light weight, corrosion resistance and ease of processing. Current interest to improve the thermal conductivity of polymers is focused on the selective addition of nanofillers with high thermal conductivity. Unusually high thermal conductivity makes carbon nanotube (CNT) the best promising candidate material for thermally conductive composites. However, the thermal conductivities of polymer/CNT nanocomposites are relatively low compared with expectations from the intrinsic thermal conductivity of CNTs. The challenge primarily comes from the large interfacial thermal resistance between the CNT and the surrounding polymer matrix, which hinders the transfer of phonon dominating heat conduction in polymer and CNT. This article reviews the status of worldwide research in the thermal conductivity of CNTs and their polymer nanocomposites. The dependence of thermal conductivity of nanotubes on the atomic structure, the tube size, the morphology, the defect and the purification is reviewed. The roles of particle/polymer and particle/particle interfaces on the thermal conductivity of polymer/CNT nanocomposites are discussed in detail, as well as the relationship between the thermal conductivity and the micro- and nano-structure of the composite
