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.