Theoretical as well as observational aspects of the s-process nucleosynthesis are reviewed. The classical site-independent s-process model as well as the s-process in massive stars are shortly described. A special attention is paid to the nucleosynthesis taking place in AGB stars and the extra-mixing invoked to explain the production of neutrons in the C-rich layers during the interpulse. We also discuss the nucleosynthesis found in hot AGB stars for which the s-process during the interpulse phase is inhibited, but the one resulting from the large temperatures in the thermal pulse is boosted. We comment on the uncertainties affecting our understanding of the physical mechanisms responsible for a successful s-process. Finally, various types of spectroscopic observations of s-process elements are discussed.