Spun fibers are one of the most viable solutions to polarization mode dispersion. In this paper, their polarization properties are reviewed with special emphasis on randomly birefringent strongly spun fibers. The analysis is carried out by means of a new simplified model, which applies to a wide range of spin profiles that are either deterministic or random. It is shown that in general, a strongly spun fiber is characterized by an apparent random linear birefringence and an apparent deterministic circular birefringence. The latter term may originate unusual polarization properties; yet, in some cases of practical interest, it is equal to zero, and when this happens, the strongly spun fiber has the same statistical properties of an unspun on...