The state-of-art and key problems of carbon nanotube (CNT) based polymer composites (CNT/polymer composites) including CNT/polymer structural composites and CNT/polymer functional composites are reviewed. Based on the results reported up to now, CNTs can be an effective reinforcement for polymer matrices, and the tensile strength and elastic modulus of CNT/polymer composites can reach as high as 3600 MPa and 80 GPa, respectively. CNT/polymer composites are also promising functional composite materials with improved electrical and thermal conductivity, etc. Due to their multi-functional properties, CNT/polymer composites are expected to be used as low weight structural materials, optical devices, thermal interface materials, electric components, electromagnetic absorption materials, etc. However, the full potential of CNT/polymer composites still remains to be realized. A few key problems, such as how to prepare structure-controllable CNTs with high purity and consistently dependable high performance, how to break up entangled or bundled CNTs and then uniformly disperse and align them within a polymer matrix, how to improve the load transfer from matrix to CNT reinforcement, etc, still exist and need to be solved in order to realize the wide applications of these advanced composites