Abstract: Teichmueller curves are complex geodesics in the moduli space of curves with respect to the Kobayashi metric. As such, a Teichmueller curve in genus 2 moduli space naturally parametrizes a family of Kummer K3 surfaces. We will discuss the geometry of such a family of K3 surfaces arising from Teichmueller curves, with special emphasis on the variation of Hodge structure and mirror symmetry. Time permitting, we will talk about 'attractive' K3 surfaces, which are special fibers of this family, that provide a fascinating link between the arithmetic theory of complex multiplication and black holes in type IIB string theory compactified on the product of a K3 surface with an elliptic curve (This is ongoing work with Atish Dabholkar (ICTP)).