Polarization of solar lines arises due to illumination of radiating atom by anisotropic (limb darkened/brightened) radiation. Modelling the polarized spectra of the Sun and stars requires solution of the line radiative transfer problem in which the relevant polarizing physical mechanisms are incorporated. The purpose of this paper is to describe in what different ways the polarization state of the radiation `complicates' the numerical methods originally designed for scalar radiative transfer. We present several interesting situations involving the solution of polarized line transfer to prove our point. They are (i) Comparison of the polarized approximate lambda iteration (PALI) methods with new approaches like Bi-conjugate gradient method that is faster, (ii) Polarized Hanle scattering line radiative transfer in random magnetic fields, (iii) Difficulties encountered in incorporating polarized partial frequency redistribution (PRD) matrices in line radiative transfer codes, (iv) Technical difficulties encountered in handling polarized specific intensity vector, some components of which are sign changing, (v) Proving that scattering polarization is indeed a boundary layer phenomenon. We provide credible benchmarks in each of the above studies. We show that any new numerical methods can be tested in the best possible way, when it is extended to include polarization state of the radiation field in line scattering.