I will talk about recent results on the interplay between internal (e.g. star formation, stellar feedback) and external (gas accretion, halo/environmental quenching, mergers) processes affecting the growth of the stellar component of galaxies.
I will first show that, to the zero-th order, galaxy evolution is a relatively simple self-regulating process that can be understood in terms of balance between inflows and outflows at a given star formation efficiency. These simultaneously determine the evolution of the specific star formation rate (sSFR) and the metallicity across cosmic times, and - at a fixed time - explain the mass-metallicity-SFR relation observed in galaxies.
I then highlight some recent empirical results on the effect of mergers in enhancing the (s)SFR of interacting galaxies as a function of mass and environment.
Finally, I present some work in progress with semi-analytic models. In particular I compare their predictions to the latest observations of the passive fraction in groups, as well as to the galaxy mass function and the sSFR evolution over cosmic time. I present successes and failures of such approach, and suggest the way to improve these models.