The recent discovery of microscopic grains of presolar origin in primitive meteorites has opened a new field of astrophysics where scientists from different disciplines, from nuclear physics to astronomy, chemistry and mineralogy, are required to work together. In this inter-disciplinary field information on the composition of stars is obtained through laboratory analysis of meteoritic rocks. We review the main features of the composition of presolar SiC and oxide grains that are believed to have originated in Asymptotic Giant Branch (AGB) stars. High-precision laboratory measurements of the isotopic composition of these types of presolar grains represent the most detailed record of the composition of AGB stars, and thus a major constraint for the theoretical models of these stars. In particular, the CNO and Al/Mg compositions can set constraints on extra-mixing processes in red giant and AGB stars. The composition of heavy elements produced by slow neutron captures (s-process) yields a variety of information on the grain parent stars, including their masses and the way neutron sources operate.