Asymptotically Conical (AC) Calabi-Yau manifolds are Ricci-flat Kahler manifolds that resemble a Ricci-flat Kahler cone at infinity. The first result I will present is a refinement of an existence theorem of Tian and Yau from the early ´90´s for these manifolds.

In more recent years, new examples of "irregular" Calabi-Yau cones have been discovered by mathematicians and physicists alike. I will also present the first example of an AC Calabi-Yau metric on a smoothing of such a Calabi-Yau cone.

This is joint work with Hans-Joachim Hein (Nantes).