This manuscript presents a synthesis of my research on reconstructing the star-formation histories (SFH) of galaxies and understanding the physical processes that shape their evolution across cosmic time. Central to this work is the relation between the star-formation rate and stellar mass, the so-called Main Sequence of star-forming galaxies (MS). I developed methods to constrain how galaxies evolve within this plane, whether through secular processes, stochastic bursts, or rapid quenching episodes, from the local Universe to the highest accessible redshifts. This work relies on the development and application of advanced spectral energy distribution (SED). I contributed to the implementation of SFH enabling the reconstruction of both long-term evolutionary trends and short- timescale variations in star-formation activity. These tools were used to identify and characterise rapid quenching events, investigate their multi-wavelength signatures, particularly in the infrared and radio, and constrain the physical mechanisms driving these abrupt changes. In particular, I employed these methods to investigate the nature and evolution of compact “starbursts within the Main Sequence”, showing that despite their extreme gas depletion, their recent SFHs are indistinguishable from those of other MS galaxies, suggesting a self- regulated evolutionary path. Finally, I examined galaxy evolution within the first gigayear, demonstrating that galaxies at z>6 exhibit highly diverse and often strongly bursty SFHs, with a transition from stochastic to secular star formation emerging around z~9. In other words, my research aims to reconstruct the star-formation histories of galaxies from their spectral emission and to use these histories as powerful diagnostics of the physical processes that govern galaxy evolution across the history of the Universe.
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