Caldararu's conjecture (now a Theorem) states that the Hochschild-Kostant-Rosenberg quasi-isomorphism on a complex manifold $X$, appropriately composed with actions of the Atiyah class of $X$, yields a quasi-isomorphism of dg-algebras between the Dolbeault cohomology of holomorphic polyvector fields/forms on $X$ and the Hochschild (co)homology of $X$: this result can be proved by using methods coming from deformation quantization, i.e. Kontsevich's and Tsygan's formality results.