complete calabi-yau metrics are fundamental objects in kahler geometry arising as singularity models or "bubbles" ​in degenerations of compact calabi-yau manifolds.  the existence of these metrics and their relationship with algebraic geometry are the subjects of several long standing conjectures due to yau and tian-yau.  i will describe some recent progress towards the question of existence, and explain some future directions, highlighting connections with notions of algebro-geometric stability.​