  Nuclear reaction cross sections are essential ingredients to predict the
evolution of AGB stars and understand their impact on the chemical evolution of
our Galaxy. Unfortunately, the cross sections of the reactions involved are
often very small and challenging to measure in laboratories on Earth. In this
context, major steps forward were made with the advent of underground nuclear
astrophysics, pioneered by the Laboratory for Underground Nuclear Astrophysics
(LUNA). The present paper reviews the contribution of LUNA to our understanding
of the evolution of AGB stars and related nucleosynthesis.
