I will discuss the implications of implementing a two independent variable Initial Mass Function (IMF) scenarios in semi-analytic models. These approaches provides a description of the dependence of the stellar IMF shape on the physical properties of model galaxies (either the SFR or the SFR surface density). In the framework of the GAEA (GAlaxy Evolution and Assembly) model, which features a detailed treatment of chemical enrichment and stellar feedback, I will show that realizations with a universal IMF predict a rather flat alpha/Fe-stellar mass relation. The models assuming a variable IMF, instead, are able to reproduce the observed increase of alpha-enhancement with stellar mass. This is mainly due to the fact that massive galaxies are characterized by larger star formation rates at high-redshift, leading to stronger alpha-enhancement with respect to low-mass galaxies. At the same time, the final stellar masses and mass-to-light-ratio of our model galaxies are larger than those estimated from the synthetic photometry assuming a universal IMF, providing a self-consistent interpretation of recent claims for IMF variations in massive galaxies, based on dynamical analysis of local early type galaxies. Indeed, the different variable IMF scenarios does not affect significantly the trend for shorter star formation timescales for more massive galaxies, but they can change significantly their star formation histories. Nonetheless, the definition of observational tests able to discriminate between these scenarios is challenging even for the next generation facilities.