The Teichmueller space of a finite type Riemann surface is abundantly populated by holomorphic disks, isometric to the complex hyperbolic line of curvature -4 for their Kobayashi-Teichmueller metrics, known as Teichmueller disks. In this talk we will show that any isometric disk must be holomorphic, hence a Teichmueller disk. This answers a long-standing question in the subject. Depending on time we will continue our discussion about totally geodesic subsets, showing that the image of a totally-geodesic holomorphic map from a Kaehler manifold into Teichmueller space must be a Teichmueller disk as well.