Carbon nanotubes (CNTs) have been used in making composites because CNTs have high strength, large aspect-ratio and excellent thermal and electrical conductivity. However, to realize the wide applications of CNT composites, further R&D must be carried out. This review will discuss some fabrication, characterisation and application issues of CNT polymer composites. Aspects to outline are purification, dispersion, alignment, stress transfer, interface bonding, wear and friction and rheological properties. Some research challenges will be briefly highlighted as well, including the mass production of long and aligned CNTs at low cost, and the optimization of the microstructures, properties and functioning features of CNT composites.