Abstract: I will discuss the general problem of understanding collapsed limits of Ricci-flat Kahler metrics on a compact Calabi-Yau manifold when the Kahler class degenerates to the boundary of the Kahler cone. I will discuss some positive results (joint with Hein) when the limiting class is the pullback of a Kahler class from the base of a holomorphic fibration, and some negative results (joint with Filip) when the limiting class is not of this form.