  This paper addresses the modelling issue of the linearly-polarized solar limb
spectrum, which is due to scattering processes and it offers a rich diagnostic
potential for exploring solar magnetic fields via the Hanle effect. However,
this so-called second solar spectrum is full of mysterious spectral features,
which cannot be understood with simplified polarization transfer theories, thus
suggesting that the underlying scattering physics is more complex than
previously thought. In this paper we argue that the physical understanding of
the second solar spectrum requires the consideration of scattering processes in
multilevel atomic models, taking fully into account the transfer of atomic
polarization among all the levels involved. The consideration of lower-level
atomic polarization leads to non-linear and non-local coupled sets of
equations, even for the two-level model atom case considered in this paper. The
unknowns of the problem are the irreducible tensor components of the atomic
density matrix whose self-consistent values have first to be obtained to be
able to calculate the emergent Stokes profiles. To solve numerically this
non-LTE problem of the second kind we present some iterative methods that are
very suitable for developing a general multilevel scattering polarization code.
We demonstrate that there exists metastable-level atomic polarization in the
solar chromosphere, which suggests that the solution to some
recently-formulated "paradoxes" is to be found by carefully revising our
current ideas about the chromospheric magnetic field.
