In this talk, we study  the Gromov-Hausdorff convergence of  Ricci-flat metrics   under degenerations of Calabi-Yau manifolds. More precisely, for a family of polarized Calabi-Yau manifolds degenerating to a singular Calabi-Yau variety,  we prove that  the Gromov-Hausdorff limit of Ricci-flat kahler metrics on them is unique.