Most technologically useful materials are polycrystalline, composed of many small crystallites called grains separated by interfaces called grain boundaries. These grain boundaries play a role in many material properties, for example conductivity and fracture toughness, and across many scales. Preparing arrangements or distributions of boundaries suitable for a given purpose is a central problem in materials. It is, indeed, the central problem of microstructure and has an extensive history dating from prehistory. Grain growth is one of the primary microstructural mechanisms. We may ask many questions, for example, to what extent is grain growth like or unlike the growth of soap bubbles. We discuss some of the scientific challenges we encounter in the investigation of these issues. In recent years we have been able to begin simulations at mesoscale which are both accurate and statistically significant, that is, they are very large scale. What is the ’answer’ of such a simulation? This is a very pregnant question. We present various results and surprises, but primarily we expose the rich trove of problems this study is unveiling. This is joint work with Florin Manolache, Jeehyun Lee, Irene Livshits, Gregory Rohrer, Anthony Rollett, and Shlomo Ta’asan. [1] Partially supported by the NSF under the MRSEC program.