Newton polygons are one of the most important invariants to study Shimura varieties, a central topic in arithmetic geometry. The cohomology of corresponding strata is the main tool to realize local Langlands correspondences. In this talk I will report on the geometry of Newton strata in Shimura varieties and loop groups. Here, even basic questions such as non-emptiness or dimensions of strata were only answered very recently, and that although the answers yield concise and elegant formulas.