Galaxy spectra encode a vast amount of information concerning the underlying stellar populations that allow us to explore the evolution of galaxies. I will give a general overview of how population synthesis has allowed us to understand  fundamental processes in extragalactic astrophysics and what major hurdles  prevent us from retrieving detailed formation histories from spectra. I will contrast standard methodology (based on model fitting) with data-driven  approaches (adopting multivariate analysis, information theory or machine learning methods), presenting some recent results related to the way local and global factors  affect galaxy formation.