Over the past decade, it has become increasingly clear that the Gromov-Hausdorff limits of Kähler manifolds, particularly in the non-collapsing case, possess deep connections with algebraic geometry. In the context of moduli theory, M. de Borbon and C. Spotti have proposed the "multiscale K-moduli problem" as an algebro-geometric framework to describe algebro-geometric aspects of "bubbling limits" of Kähler-Einstein metrics. In this talk, after providing an overview of general results regarding the limits of polarized Kähler-Einstein manifolds, I will discuss the multi-scale K-moduli problem specifically for the case of non-collapsing polarized K3 surfaces.