This paper considers the problem of modeling the light polarization that emerges from an astrophysical plasma composed of atoms whose excitation state is significantly influenced by the anisotropy of the incident radiation field. In particular, it highlights how radiative transfer simulations in three-dimensional models of the “quiet” solar atmosphere may help us to probe its thermal and magnetic structure, from the near equilibrium photosphere to the highly non-equilibrium upper chromosphere. The paper finishes with predictions concerning the amplitudes and magnetic sensitivities of the linear polarization signals produced by scattering processes in two transition region lines, which should encourage us to develop UV polarimeters for sounding rockets and space telescopes with the aim of opening up a new diagnostic window in astrophysics.