This article presents an introduction to optical pumping, atomic polarization and the Hanle effect in weakly magnetized stellar atmospheres. Although the physical processes and the theoretical framework described here are of interest for applications in a variety of astrophysical contexts (e.g. scattering polarization in circumstellar envelopes and polarization in astronomical masers), the article focuses mainly on the quest for understanding the physical origin of the linearly polarized solar limb spectrum. It considers also the development of the Hanle effect as a reliable diagnostic tool for making feasible new advances in solar photospheric and chromospheric magnetism. Particular emphasis is given to a rigorous modeling of polarization phenomena as the essential link between theory and observations. Some of the most recent advances in this field are presented after carefully explaining how the various radiation pumping mechanisms lead to atomic polarization in the absence and in the presence of weak magnetic fields.