When polarized light is coupled into an ideally straight strain-free circularly symmetric single-mode fiber, the state of polarization (SOP) is maintained along the fiber. In real fibers, however, the SOP changes rapidly, typically after propagation through a fraction of a meter. These changes result from the simultaneous existence of two modes of orthogonal polarizations in the single-mode fiber. Their propagation is modified in different ways by effects internal to the fiber (noncircular core, internal stress) and by external effects (lateral pressure, twisting, bending, and magnetic and electric fields). The real fiber, therefore, is birefringent.