Owing to their unique mechanical properties, carbon nanotubes are considered to be ideal candidates for polymer reinforcement. However, a large amount of work must be done in order to realize their full potential. Effective processing of nanotubes and polymers to fabricate new ultra-strong composite materials is still a great challenge. This Review explores the progress that has already been made in the area of mechanical reinforcement of polymers using carbon nanotubes. First, the mechanical properties of carbon nanotubes and the system requirements to maximize reinforcement are discussed. Then, main methods described in the literature to produce and process polymer–nanotube composites are considered and analyzed. After that, mechanical properties of various nanotube–polymer composites prepared by different techniques are critically analyzed and compared. Finally, remaining problems, the achievements so far, and the research that needs to be done in the future are discussed.