  It is well known that thermally pulsing Asymptotic Giant Branch stars with
low mass play a relevant role in the chemical evolution. They have synthesized
about 30% of the galactic carbon and provide an important contribution to the
nucleosynthesis of heavy elements (A>80). The relevant nucleosynthesis site is
the He-rich intermediate zone (less than 10^{-2} Msun), where
alpha(2alpha,gamma)12C reactions and slow neutron captures on seed nuclei
essentially iron) take place. A key ingredient is the interplay between nuclear
processes and convective mixing. It is the partial overlap of internal and
external convective zones that allows the dredge-up of the material enriched in
C and heavy elements. We review the progresses made in the last 50 years in the
comprehension of the s process in AGB stars, with special attention to the
identification of the main neutron sources and to the particular physical
conditions allowing this important nucleosynthesis.
