On complex symmetric spaces of rank one, Stenzel constructed explicit examples of Calabi-Yau metrics with smooth cross-section asymptotic cone. The classification of such metrics has been achieved by Conlon-Hein, but such a general result remains unsolved when the cone has singular cross-section. A new feature in higher rank symmetric spaces is that the possible candidates for asymptotic cones pratically have singular cross-section. After an introduction and survey of known results, I will present an existence theorem of Calabi-Yau metrics on symmetric spaces of rank two with all asymptotic cone having singular cross-section. This covers the rank two symmetric spaces left by Biquard-Delcroix, achieving the classification of exact Calabi-Yau metrics with maximal volume growth on these spaces. If time allows, I will also try to explain why some special symmetric spaces of rank two don't have any invariant Calabi-Yau metrics with a given asymptotic cone, using an obstruction on the valuation induced by such metric if exists.