Abstract: I will first briefly describe different ways of modeling the vehicle traffic flow, from microscopic i.e. large systems of ODEs, called “Follow-the-leader” models (FLM), to macroscopic (fluid) models. I will then introduce a class of (“second order”) models that we introduced a few years ago with Aw, in order to cure the (huge) draw-backs of models based on gas dynamics. Indeed, assimilating cars (and drivers) to particles of gas predicts in some cases cars moving backwards … I will show how one can cure this model in a very simple way, by assuming that the response of each class of cars is determined both by the local density and by (Lagrangian) properties of this class. In fact, this class of models can be rigorously derived from the microscopic FLM models. Finally, if time allows, I will indicate how such models can be homogenized, in a simple but non-trivial way, when the reactions of car-driver pairs are highly oscillating. This is in particular highly relevant when we want to study a network, and therefore describe the coupling between the incoming and the outgoing roads at a junction.