The talk will overview two prototypical problems of multiscale computational science for which a mathematical approach can help. Both topics are related to materials science in a broad sense. The first topic is multiscale-in-space in nature: random composite materials are often prohibitively expensive to simulate numerically. A category of new, efficient numerical approaches that elaborates on the possibly small disorder present in such materials will be described. The second topic is multiscale-in-time in nature: the efficiency of the parallel replica method, simulating long term dynamics of potentially metastable evolutions, will be examined mathematically. The talk is joint work with a number of colleagues from Ecole des Ponts, INRIA, and several other institutions.