In the last few years, tropical methods have been applied quite successfully in understanding the combinatorics behind compactifications of moduli spaces, in particular by endowing them with a tropical modular interpretation. Consequently, one can study different properties of these (compactified) spaces by studying their tropical counterparts. In this talk, which is based in joint work with Madeleine Brandt, Juliette Bruce, Melody Chan, Gwyneth Moreland and Corey Wolfe, I will illustrate this phenomena for the moduli space A_g of abelian varieties of dimension g. In particular, I will show how to apply the tropical understanding of the classical toroidal compactifications of A_g to compute, for small values of g, the top weight cohomology of A _g. We also show that our results can be used to study the stable cohomology of the Satake compactification of A_g and the