Asymptotically conical Calabi-Yau manifolds are a special class of complete Ricci-flat K\”ahler manifold that are asymptotic to a cone at infinity. They often appear as blow-up limit for degenerations of non-collapsed Kahler-Einstein metrics near a singular limit, and hence serves as local models for degenerations of K\”ahler-Einstein metrics near points of large curvature. The first general analytic construction of asymptotically conical Calabi-Yau manifolds goes back to the work of Tian-Yau in the 90s, it has subsequently refined through the works of many people and is now very well developed. In this talk, I will first review the theory of asymptotically conical Calabi-Yau metrics, then I will discuss some work on the study of degenerations of asymptotically conical Calabi-Yau metrics and applications to constructing asymptotically conical Calabi-Yau metrics with singularities. This is joint work with Tristan Collins and Bin Guo.