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 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 "see" magnetic fields to which the Zeeman effect is blind within the limitations of the available instrumentation. This lecture reviews some of the recent advances in the polarized radiation diagnostic methods with which we may hope to decipher the complexity of the Sun's hidden magnetism (i.e., all the magnetic fields of the extended solar atmosphere that are impossible to diagnose via the only consideration of the Zeeman effect).