This paper surveys recent progress in fiber spinning technology for reducing polarization mode dispersion with the focus on theoretical understanding of fiber spinning mechanism and features of spun fibers, as well as their applications in fiber spin profiles designs. First, a brief introduction to the requirements of fiber PMD for high-speed optical fiber communications systems is given. Further discussion covers several spin technologies, including preform spinning and fiber spinning. Different theoretical approaches for modeling fiber spinning are reviewed with the emphasis on the coupled-mode formalism. The coupled-mode theory is then applied to different fiber spin profile designs, including constant, sinusoidal and frequency and amplitude modulated spin profiles. Main features of these spin profiles, such as PMD reduction dependence on fiber beatlength and sensitivity to spin parameters, are compared. Scaling properties of spun fibers, which show different behaviors from unspun fibers, are also discussed.