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 M_⊙), where α(2α,γ)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.