We explore some recent advances in the understanding of the astrophysical origin of the s-process of nuclei with atomic mass number A > 90. First we focus on how the s-process is not of unique nature, the abundance distribution in the solar system being the outcome of all previous generations of AGB stars of different masses and metallicities, each one of them providing a different s-process isotopic distribution. The necessity of using a continuously updated network of neutron capture rates is emphasized. We examine the s-process contribution by Galactic chemical evolution, including lead, and compare theoretical predictions with spectroscopic observations. A brief description of the light-s and heavy-s elements enhancements in chemically peculiar stars of different spectroscopic classes is given. A tentative interpretation of the s-element distribution of the extremely peculiar objects FG Sge, Sakurai's object, and R CrB stars is put forth. Finally, the AGB origin of meteoritic presolar SiC grains is briefly analyzed.