We present asymptotic giant branch (AGB) models of solar metallicity, to allow the interpretation of observations of Galactic AGB stars, whose distances should be soon available after the first release of the Gaia catalogue. We find an abrupt change in the AGB physical and chemical properties, occurring at the threshold mass to ignite hot bottom burning, i.e. 3.5 M⊙. Stars with mass below 3.5 M⊙ reach the C-star stage and eject into the interstellar medium gas enriched in carbon, nitrogen and 17O. The higher mass counterparts evolve at large luminosities, between 3 × 104 and 105 L⊙. The mass expelled from the massive AGB stars shows the imprinting of proton-capture nucleosynthesis, with considerable production of nitrogen and sodium and destruction of 12C and 18O. The comparison with the most recent results from other research groups is discussed, to evaluate the robustness of the present findings. Finally, we compare the models with recent observations of galactic AGB stars, outlining the possibility offered by Gaia to shed new light on the evolution properties of this class of objects.