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We survey some recent developments in the study of collapsing Riemannian manifolds with Ricci curvature bounded below, especially the locally bounded Ricci covering geometry and the Ricci flow smoothing techniques. We then prove that if a Calabi-Yau manifold $M$ is sufficiently volume collapsed with bounded diameter and sectional curvature, then there is a nearby Ricci-flat Kahler metric on $M$ together with a compatible pure nilpotent Killing structure - this is related to an open question of Cheeger, Fukaya and Gromov.

Collapsing Geometry with Ricci Curvature Bounded Below and Ricci Flow Smoothing