Semi-empirical models of galaxy formation and evolution

We provide a review on semi-empirical models of galaxy formation and evolution. First we present a brief census of the three main modeling approaches to galaxy evolution, namely hydrodynamical simulations, semi-analytic models, and semi-empirical models (SEMs). Then we focus on SEMs in their different flavors, i.e., interpretative, descriptive and hybrid, discussing the peculiarities and highlighting virtues and shortcomings for each of these variants. Moreover, we dissect a simple and recent hybrid SEM from our team to highlight some technical aspects. Finally, we offer some outlook on the prospective developments of SEMs, and we provide a short summary of this review.