Abstract: In the last few years, it has been understood that nice algebro-geometric moduli spaces can be ?tropicalized? via modular maps which allow to study many properties of the original spaces by looking at their tropical counterpart. Often, a first step is to give a tropical interpretation to combinatorial data used to compactify. In the presence of such a relation, one can use the tropical modular interpretation to study geometric properties of the original space. In the talk, I will try to explain this interplay in the case of curves, (universal) Jacobians and the moduli space of abelian varieties. I will then try to explain how to use the tropical moduli spaces to compute the top weight rational cohomology of the original algebro-geometric spaces.