%0 Journal Article %T Formality theorems for Hochschild complexes and their applications %A V. A. Dolgushev %A D. E. Tamarkin %A B. L. Tsygan %J Mathematics %D 2008 %I arXiv %R 10.1007/s11005-009-0350-3 %X We give a popular introduction to formality theorems for Hochschild complexes and their applications. We review some of the recent results and prove that the truncated Hochschild cochain complex of a polynomial algebra is non-formal. %U http://arxiv.org/abs/0901.0069v2