Asymptotic Giant Branch (AGB) stars are among the most important astrophysical sites influencing the nucleosynthesis and the chemical abundances in the Universe. From a pure nuclear point of view, several processes take part during this peculiar stage of stellar evolution thus requiring detailed experimental cross section measurements. Here, we report on the most recent results achieved via the application of the Trojan Horse Method (THM) and Asymptotic Normalization Coefficient (ANC) indirect techniques, discussing the details of the experimental procedure and the deduced reaction rates. In addition, we report also on the on going studies of interest for AGB nucleosynthesis.