  We determine the cone of nef divisors on the Igusa and Voronoi
compactifications of the moduli space of principally polarised abelian 4-folds.
We also show that the canonical bundle on the Igusa compactification of A_4(n)
is ample for n at least 3. Analogous results for A_2 and A_3 were earlier
obtained by the first author but the case of A_4 is far less simple.
