Ultraoriented polymer fibers have elastic modulus E as large as 350 GPa and tensile strength sigma(b) as large as 7 GPa in materials with a density rho approximate to 1200 Kg/m(3). Keys to achieving these properties are near perfect orientation of polymer chains along the fiber axis and reduction of the number of chain ends. The two materials that have been most thoroughly studied are polyethylene (PE) and poly(p-phenylene terephthalamide) (PPTA). Various schemes for calculating the elastic modulus are reviewed, together with estimates of effects of imperfect chain orientation and the presence of chain ends. Fracture of fibers is treated in terms of covalent bond scission and/or chain slip originating at chain ends. Under laboratory conditions the experimental modulus E can be >90% of the theoretical modulus. It appears that fracture is more sensitive to chain end defects, limiting practical strength to less than 25% of the ultimate strength predicted from bond scission models.