We will review a set of works devoted to the numerical simulation of multiscale materials. One line of research described aims at making multiscale finite element methods more versatile and robust, so that they can efficiently adjust to variations of geometries and microstructures, random parameters, etc. A second set of contributions presented addresses the cases when only little information on the internal structure of the material is accessible : a novel numerical approach is introduced to construct an effective model, combining ideas from optimization, model reduction and statistics.