Abstract 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. To control it we must understand grain growth. For example, to what extent is grain growth like or unlike the growth of soap bubbles? In this expository talk we discuss some of the scientific challenges we encounter in the investigation of these issues. What are the strategies for determining interfacial energy? Can we simulate large grain networks? We address the mesoscale simulation of large systems. What is the 'answer' of such a simulation? This is a very pregnant question. This is joint work with Florin Manolache, Jeehyun Lee, Irene Livshits, Anthony Rollett, and Shlomo Ta'asan.