Abstract: The phase shifts experienced by a polarized light wave when it propagates through media with arbitrary birefringence, dichroism and depolarizing properties, while on the one hand provide the basis for a variety of optical devices and experiments, on the other provide a powerful means of understanding unitary evolution, nonunitary evolution and decoherence of two-state quantum systems by virtue of a mathematical isomorphism of the two systems. These also help understand aspects of evolution of classical systems under the group of rotations in three-dimensional space, namely the SO(3) group, by virtue of its homomorphism with the group SU(2) governing unitary evolution of polarized light waves. In this review we present a survey and analysis of recent work on topological phases with polarization of light which has revealed several counterintuitive features of such phase shifts such as 2 nπ anholonomies, nonlinear and discontinuous behaviour originating hi singularities, peculiar spectral dependence, etc. We point out several areas where these results may find practical application, for example endless phase correction in interferometric sensors, fast switching spatial light modulators, phase shifters with unusual chromatic properties, phasing of antenna arrays, etc. Several useful theoretical insights relevant to polarization optics, quantum mechanics, classical mechanics and other areas of physics, obtained from the work on polarization states are described and some directions for future work are indicated.