For the development of a realistic model of the formation and evolution of galaxies is necessary a systematic comparison with observations.  This aspect is crucial since a discrepancy is indicative of a lack from the point of view of physical processes and of the values assigned to the free parameters in the construction of the model.  In this work we analyze some of the semi-analytical models of galaxy formation (Merson et al. 2013, Henriquez et al. 2013, 2014, De Lucia & Blaizot 2007, Monaco et al. 2006, Guo et al. 2013), making use of the redshift evolution of the stellar mass function of galaxies (MF) as statistical tool indicative of the quenching history of galaxies.  They were compared (using mocks to test sample selection effects) to MFs at 0<z<3 derived from observations (SDSS, BOSS, zCOSMOS, VIPERS, VVDS, COSMOS, etc), to probe the effects of various modeling of physical processes.  In addition, models are compared separately for star-forming galaxies and passive galaxies, by adopting different criteria (based on the specific star formation rate and/or on the specific color), also to assess the effects of that choice. Finally we evaluated the evolution with cosmic time of the number densities, in particular of quiescent galaxies in various ranges of mass, and the redshift at which their number densities are halved to explore the differences between models and observations about the timing of their quenching and assembly history according to their mass.