This talk gives an overview of the computational and analytical issues underpinning mathematical modeling of polycrystalline materials on multiple spatial and temporal scales for advancing materials design and engineering. There is a number of challenges to be faced, including the development of fast yet reliable simulation techniques for prediction of microcracking and irreversible damage in materials caused by environmental factors, as well as the design of efficient methods for analyzing vast amounts of data recently made available by advances in experimental design and instrumentation.