Theoretical approaches to the physics of spectral line polarization

Due to the continuous developments in polarimetric instrumentation, which will become even more dramatic in the near future with the availability of new generation solar telescopes, we are now severely confronted with a variety of new detailed observations of high diagnostic potential, whose interpretation requires a firmly established theoretical framework. In this contribution, I review the fundamental physical processes that underlie the generation and transfer of polarized radiation in stellar atmospheres, and I discuss the present status of the theoretical schemes now available, pointing out their main successes and limitations. I also present some ideas about the theoretical improvements that I consider necessary to achieve a correct interpretation of the complex phenomenology shown by polarimetric observations, focusing particularly on the second solar spectrum, which can be considered as one of the most important test benches of the theory.