Polarized light provides the most reliable source of information at our disposal for diagnosing the physical properties of astrophysical plasmas, including the magnetic fields of the solar atmosphere. The interaction between radiation and hydrogen plus free electrons through Rayleigh and Thomson scattering gives rise to the polarization of the stellar continuous spectrum, which is very sensitive to the medium's thermal and density structure. Anisotropic radiative pumping processes induce population imbalances and quantum coherences among the sublevels of degenerate energy levels (that is, atomic level polarization), which produce polarization in spectral lines without the need of a magnetic field. The Hanle effect caused by the presence of relatively weak magnetic fields modifies the atomic polarization of the upper and lower levels of the spectral lines under consideration, allowing us to detect magnetic fields to which the Zeeman effect is blind. After discussing the physical origin of the polarized radiation in stellar atmospheres, this paper highlights some recent developments in polarized radiation diagnostic methods and a few examples of their application in solar physics.