This paper presents an overview of the radiative transfer problem of calculating the spectral line intensity and polarization that emerges from a (generally magnetized) astrophysical plasma composed of atoms and molecules whose excitation state is significantly influenced by radiative transitions produced by an anisotropic radiation field. The numerical solution of this non-LTE problem of the 2nd kind is facilitating the physical understanding of the second solar spectrum and the exploration of the complex magnetism of the extended solar atmosphere, but much more could be learned if high-sensitivity polarimeters were developed also for the present generation of night-time telescopes. Interestingly, I find that the population ratio between the levels of some resonance line transitions can be efficiently modulated by the inclination of a weak magnetic field when the anisotropy of the incident radiation is significant, something that could provide a new diagnostic tool in astrophysics.