Invited review abstract

A long-standing issue in solar astrophysics concerns the strength and structure variations with height of the magnetic field in the quiet chromosphere. This boundary region in the solar outer atmosphere is important, not only because it is the region where the dominant physics changes from hydrodynamic to magnetic forces and most of the non-radiative heating takes place, but also because the dissipation of magnetic energy in the overlying corona may be significantly modulated by the actual physical conditions in the chromosphere. Unfortunately, our empirical knowledge on the magnetism of the quiet solar chromosphere has remained vague notwithstanding the qualitative information provided by high resolution monochromatic images of the solar atmosphere taken at various wavelengths across strong spectral lines like H${\alpha}$ and the IR triplet of Ca {\sc ii}. Here I review some recent advances in the development and application of polarized radiation diagnostics to infer the mean magnetization of the quiet solar atmosphere, from the near equilibrium photosphere to the highly nonequilibrium upper chromosphere. My talk will probably finish with a brief summary of some ongoing plans and developments aiming at facilitating new breakthroughs in the exploration of solar magnetic fields via spectropolarimetry.