We highlight the main results of a three-dimensional (3D) multilevel radiative transfer investigation about the solar disk-center polarization of the Ca ii 8542 Å line. First, through the use of a 3D model of the solar atmosphere, we investigate the linear polarization that occurs due to the atomic level polarization produced by the absorption and scattering of anisotropic radiation, taking into account the symmetry-breaking effects caused by its thermal, dynamic, and magnetic structure. Second, we study the contribution of the Zeeman effect to the linear and circular polarization. Finally, we show examples of the Stokes profiles produced by the joint action of the atomic level polarization and the Hanle and Zeeman effects. We find that the Zeeman effect tends to dominate the linear polarization signals only in the localized patches of opposite magnetic polarity, where the magnetic field is relatively strong and slightly inclined; outside such very localized patches, the linear polarization is often dominated by the contribution of atomic level polarization. We demonstrate that a correct modeling of this last contribution requires taking into account the symmetry-breaking effects caused by the thermal, dynamic, and magnetic structure of the solar atmosphere, and that in the 3D model used the Hanle effect in forward-scattering geometry (disk-center observation) mainly reduces the polarization corresponding to the zero-field case. We emphasize that, in general, a reliable modeling of the linear polarization in the Ca ii 8542 Å line requires taking into account the joint action of atomic level polarization and the Hanle and Zeeman effects.