With the radiative transfer equation for polarized light to hand, we shall proceed to find solutions and to exploit them both, the equation and its solutions, in order to obtain information about the medium. This chapter is devoted to solutions of the RTE and to the first and simplest diagnostics one can obtain from the observed Stokes profiles. The main emphasis is on concepts rather than numerical details. The latter may be found in the literature (some of the most recent papers are recommended in the bibliography) and in fact are still in continuous evolution and debate. Most of the concepts we describe in this chapter, however, may be said to be well founded nowadays and will help the reader in understanding the topic.