Hao Fu is a PhD student at the School of Physics and Astronomy, University of Southampton. He received his MSc at Sapienza University of Rome in 2019, with the thesis research on the cosmic microwave background carried out at Paris Institute of Astrophysics. After that, he started his PhD at the University of Southampton. His research focuses on the formation and evolution of galaxies within dark matter haloes via semi-empirical models.In a dark matter-dominated Universe, where structures grow hierarchically, galaxies are thought to live inside dark matter haloes with their evolution being intimately connected. In traditional models of galaxy evolution, galaxies build up their stellar mass via the interplay among several physical processes such as mergers, star formation and quenching, implying that all the observables characterizing galaxy evolution should be strictly linked to each other. These quantities include, for example, the galaxy stellar mass function, merger rates, star formation histories, satellite abundances and intracluster light. The failure in simultaneously fitting distinct observational probes may be attributed to shortcomings in the underlying modelling, or to disagreements in different data sets. In this talk, I will present DECODE, the Discrete statistical sEmi-empiriCal mODEl, and its contribution to the field of galaxy evolution. I will show a holistic perspective among all the aforementioned quantities in galaxy evolution built via my semi-empirical approach, discussing the role of each involved physical quantity. Finally, I will present my ongoing research on the role of various quenching mechanisms in the stellar mass assembly histories of galaxies.