Understanding the physical mechanisms driving the formation and evolution of galaxies in a cosmological context represents one of the most important yet unresolved questions of modern astrophysics. Different methods have been developed over the years to link the physical properties of galaxies to the dark matter haloes in which they reside. I will give a brief overview of the aims and limits of these methods, with particular emphasis on semi-analytic models of galaxy formation. I will then review recent developments of our model for GAlaxy Evolution and Assembly (GAEA), and discuss the role of various physical processes in shaping the measured evolution of the galaxy stellar mass function and mass metallicity relation. I will overview our recent work to include a treatment for the partition of cold gas in its atomic and molecular gas components, and a variable stellar Initial Mass Function. I will conclude by discussing open problems and future perspectives.