The sources of the tensile strength and fracture of both continuous glass fibers and discontinuous wool fibers are explored in terms of structural anisotropy, enthalpy relaxation, defect orientation, and surface inhomogeneities. The fibers are spun from the E-glass and the basaltic glass melts, respectively. It is revealed that axial stress plays an important role in enhancing the strength of the oxide glass fibers. The increase of axial stress leads to the increase of both the structural anisotropy and the defect (flaws, bubbles, striae, etc.) orientation, and hence the increase of the tensile strength. Besides the axial stress, the increase of the cooling rate also increases the tensile strength of the continuous fibers. These findings are further substantiated by annealing experiments on both continuous and wool fibers below T(g). The onset annealing temperature of the tensile strength decay is close to that of the anisotropy relaxation of the continuous fibers. The relative contributions of the different factors to the fiber strength are schematically scaled with the help of the sub-T(g) annealing.