We will present some recent mathematical and numerical contributions related to nonperiodic homogenization problems. The difficulty stems from the fact that the medium is not assumed periodic, but has a structure with a set of embedded localized defects, or more generally a structure that, although not periodic, enjoys nice geometrical features. The purpose is then to construct a theoretical setting providing an efficient and accurate approximation of the solution. The questions raised ranged from the theory of elliptic PDEs, homogenization theory to harmonic analysis and singular operators.