Poisson structures describe classical limits of quantum algebras. In this talk I will discuss higher, or categorified, deformation quantization and explain how it leads to the notion of a shifted Poisson structure. A natural source of examples of higher deformation quantization is provided by the theory of quantum groups. Thus, their classical limits have a description in terms of shifted Poisson structures that I will outline. This gives a conceptual framework for many notions appearing in the theory of quantum groups such as classical dynamical r-matrices.