Carbon nanotubes (CNTs) demonstrate remarkable electrical, thermal, and mechanical properties, which allow a number of exciting potential applications. In this article, we review the most recent progress in research on the development of CNT–polymer composites, with particular attention to their mechanical and electrical (conductive) properties. Various functionalization and fabrication approaches and their role in the preparation of CNT–polymer composites with improved mechanical and electrical properties are discussed. We tabulate the most recent values of Young's modulus and electrical conductivities for various CNT–polymer composites and compare the effectiveness of different processing techniques. Finally, we give a future outlook for the development of CNT–polymer composites as potential alternative materials for various applications, including flexible electrodes in displays, electronic paper, antistatic coatings, bullet-proof vests, protective clothing, and high-performance composites for aircraft and automotive industries.