When a sequence of Kahler-Einstein metrics develop a non-collapsing singularity in the Gromov-Hausdorff sense, it has been known that under natural assumptions the singularity is algebro-geometric. To study the singular behavior of the metric the 1st order approximation is given by tangent cones, which are also known to be algebro-geometric. To get more dynamic information on the singularity formation process one is lead to study rescaled limits, which we call ``bubbles”. They are non-compact complete Calabi-Yau spaces associated to the degeneration. I will review the above backgrounds and discuss some new results on these bubbles, which also generate questions related to algebraic geometry and Riemannian geometry.