i will discuss the problem of understanding the collapsing behavior of ricci-flat kahler metrics on a calabi-yau manifold that admits a holomorphic fibration structure, when the kahler class degenerates to the pullback of a kahler class from the base. i will present new work with hans-joachim hein where we obtain a priori estimates of all orders for the ricci-flat metrics away from the singular fibers, as a corollary of a complete asymptotic expansion.