Calabi-Yau metrics and string compactification

Yau proved an existence theorem for Ricci-flat K\"ahler metrics in the 1970's, but we still have no closed form expressions for them. Nevertheless there are several ways to get approximate expressions, both numerical and analytical. We survey some of this work and explain how it can be used to obtain physical predictions from superstring theory.
Comment: 10 pages. Version to appear in Nuclear Physics B special issue: 60 Years of Calabi Conjecture