The Thermally-Pulsating Asymptotic Giant Branch (TP-AGB) phase of stellar evolution has received attention only recently in galaxy evolution, but is now an important player in our understanding of how galaxies form and evolve. Because it is a short but very luminous phase, bright in the near-IR where dust effects are small, the TP-AGB phase is a powerful tracer of intermediate-age stars in galaxies up to high redshift. The spectral signature of TP-AGB stars as defined by population synthesis models has been detected by the Spitzer Space Telescope in high-redshift galaxies, whose spectra show an amazing similarity to spectra of local stellar populations. Even accounting for the high uncertainty affecting the theoretical modelling of this phase, stellar population models including the TP-AGB have leveraged a better determination of galaxy ages and hence stellar masses, fundamental quantities for studying galaxy formation and evolution. They have also improved the results of semi-analytic models, which can better reproduce colours and the K-band luminosity function of high-z galaxies.Comment: 11 pages, 7 figures, invited review at the conference "Why galaxies care about AGB stars. II", Vienna, 201
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