Observations both in the local universe and at high redshift have clearly shown that galaxies are characterized by a distinct bimodality of star-formation and structural properties and that is reflected in a corresponding bimodality of colors, morphology types, and specific star formation rates. Particular attention has been devoted to the so-called galaxy quenching, which refers to the sets of processes that shut down the star formation activity inside galaxies and drive the transformation of galaxies from one type of the bimodality to the other, i.e., from a star-forming galaxy to a quiescent one. The physics of quenching remains a key missing piece toward a complete picture of galaxy evolution. This thesis is broadly concerned with investigating the joint evolution of super massive black hole, star-formation and structural properties of galaxies across cosmic times, with the goal of empirically constraining the physics of galaxy quenching at cosmic noon epoch.