M. Kontsevich´s Formality Theorem is the central result of deformation quantization. It states that the Lie algebra of polydifferential Hochschild cochains on a manifold is quasi-isomorphic to its cohomology, as an L-infinity algebra. It was expected for some while that this quasi-isomorphism can be extended to a G-infinity morphism. I will (equivalently) show how to extend it to a Brace-infinity morphism. As an application, one can now understand the relation to D. Tamarkin´s approach to deformation quantization, using the formality of the little disks operad. Although this sounds very abstract, the speaker promises to draw some nice pictures.