Composite materials are used to design driveshafts when significant weight savings are sought or when traditional materials cannot be used. A satisfactory design produces a transmission for which the total weight, including intermediate supports and is minimized while satisfying several constraints. First, critical speeds of the shaft should lay outside of the range of operating speeds. This condition limits the unsupported length of the shaft and requires the use of intermediate supports. The second constraint is that the shaft should not buckle under the maximum expected torque. We should also determine the stresses in each ply and verify that failure does not occur by using a suitable criterion. Driveshaft design consists of selecting the number of intermediate supports, the shaft diameter and wall-thickness. With composites, the choice of fibers and fiber orientation are additional variables to be used for optimization. This paper review the basic theory necessary for designing composite driveshafts and optimum design procedures are discussed.