Explore a comprehensive survey on Kähler manifolds with curvature bounded below in this 42-minute lecture presented at the International Mathematical Union. Delve into key topics including Yau's uniformization conjecture and related problems, compactification of certain Kähler manifolds with nonnegative Ricci curvature, and Gromov-Hausdorff limits of Kähler manifolds. Access accompanying presentation slides for enhanced understanding of this advanced mathematical discourse.