Carbon nanotubes (CNTs) have excellent mechanical, electrical, and thermal properties, and they are considered to be potential ideal fillers in polymers to produce low weight nanocomposites of high performance. This article reviews the thermal, rheological, mechanical, and electrical properties of CNT polymer composites. The crystallization behavior of polymer nanocomposites in the presence of CNTs is discussed because it strongly influences the mechanical properties of the filled polymers. It is, then, shown that the investigation of the rheological properties of CNT composite melts is fundamental to the comprehension of the dynamics and microstructure of CNT polymer composites. New results of the linear viscoelastic behavior and steady‐shear flow of CNT polymer composites are reported and analyzed. After that, the critical issue of the transfer of the superior properties of the CNTs to the nanocomposites is reviewed and discussed. Effective reinforcement can occur only if an adequate interfacial adhesion between the phases is obtained and a stable homogeneous dispersion of the individual CNTs in the host polymer matrix is achieved. If this event occurs, CNT polymer composites show significant improvements in the mechanical properties and electrical conductivity of the polymer matrix; the literature results are summarized and discussed.