Carbon nanotubes are considered short fibers, and polymer composites with nanotube fillers are always analogues of random, short fiber composites. The real structural carbon fiber composites, on the other hand, always contain carbon fiber reinforcements where fibers run continuously through the composite matrix. With the recent optimization in aligned nanotube growth, samples of nanotubes in macroscopic lengths have become available, and this allows the creation of composites that are similar to the continuous fiber composites with individual nanotubes running continuously through the composite body. This allows the proper utilization of the extreme high modulus and strength predicted for nanotubes in structural composites. Here, we fabricate such continuous nanotube polymer composites with continuous nanotube reinforcements and report that under compressive loadings, the nanotube composites can generate more than an order of magnitude improvement in the longitudinal modulus (up to 3,300%) as well as damping capability (up to 2,100%). It is also observed that composites with a random distribution of nanotubes of same length and similar filler fraction provide three times less effective reinforcement in composites.