The evolution of the star formation activity and, thus, the assembly of the stellar content of galaxies remain at the heart of galaxy evolution studies. It is now rather well established that most galaxies form stars at a level, dictated mainly by their stellar mass and regulated by secular processes. This is seen as a Main Sequence (MS) in the Star `Formation Rate (SFR)-stellar mass plane. The normalization of this sequence declines with time since z~2, indicating an overall decrease of the star formation activity of the galaxy population in the Universe. However, we do not yet fully understand the processes that control this evolution, nor how individual galaxies evolve relative to it. While the existence of a MS may seem to suggest a simple and universal mode of star formation in galaxies (on average), the deviations indicate a more complex relation between galaxy SFRs, gas reservoir, external and internal mechanisms triggering or halting star formation. In this context I will show, with a statistical approach, how the MS evolves from the local Universe up to z~2 in slope and normalization, by using the deepest available UV and far-infrared galaxy surveys. In addition, I will discuss our results based on the Hubble Deep UV (HDUV) Survey about the interplay between environment, morphology and feedback in setting the distribution of galaxies around the MS at any redshift.