In the density matrix formalism, the ensemble of atoms or ions is expressed in terms of population and alignment of excited levels and the ground state. The population of an excited level determines the intensity of an emission line originating from this level and the alignment gives rise to the linear polarization of this line. Spatially anisotropic collisions induce transitions between the populations and the alignments; for example, an alignment along with a population is produced by a beam of electrons in an excited level from the ground-state population. Thus, an anisotropic plasma produces polarized radiations, and by plasma polarization spectroscopy (PPS) we can investigate the anisotropic, and thus non-thermal, features of the plasma. The angular distribution of the perturber velocities is expanded in terms of Legendre polynomials. The expansion coefficients and the relevant cross sections for the transitions among the populations and the alignments yield the rate coefficients for these transitions. For the ensemble of atoms or ions immersed in the plasma, coupled rate equations are constructed for the populations and the alignments of excited levels. We review the present status of our knowledge of the collision cross sections for various collision processes. Several experimental observations of PPS performed so far are reviewed, which include those on a tokamak plasma, laser produced plasmas, various discharge plasmas and solar flares. We discuss what kind of information could be obtained from PPS.