  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.
