In this contribution we propose a presentation of the Eulerian multi-fluid modeling for polydisperse evaporating sprays. The purpose of such a model is to obtain a Eulerian type of description with three main criteria : to take into account accurately the polydispersion of the spray as well as size-conditioned dynamics and evaporation, to keep a rigourous link with the Williams spray equation at the kinetic, also called mesoscopic, level of description, where the elementary phenomena such as coalescence can be described properly, to have an extension to take into account non-resolved but modeled fluctuating quantities in turbulent flows. We aim at presenting the fundamentals of the model, the associated precise set of related assumptions as well as its implication on the mathematical structure of solutions, robust numerical methods able to cope with the potential presence of singularities and finally a set of validations showing the efficiency and the limits of the model.