Carbon nanotubes demonstrate remarkable mechanical, thermal, and electrical properties, which allow a number of exciting potential applications. In this article, the most recent progress in research on the development of carbon nanotube-polymer composites is critically reviewed, with emphasis on recent advances in the principles and techniques for carbon nanotube functionalization. Various functionalization approaches and their role in the preparation of carbon nanotube-polymer composites with improved mechanical and electrical properties are discussed. The interaction between carbon nanotubes and polymers is also reviewed. Various techniques of carbon nanotube-polymer interaction measurements, including experimental and modelling studies, are described. Different methods of interaction improvement, mainly categorized under covalent and noncovalent interactions, are also described afterwards. An optimum carbon nanotube-polymer interaction is a crucial factor towards reaching the full potential of carbon nanotubes in nanocomposites. Potential topics of oncoming focus along with the potential applications of carbon nanotube-polymer composites are highlighted.