'Effective' properties of heterogeneous elastic materials are now well understood, following years of progress in homogenization and calculus of variations. For brittle materials, the situation is quite different. For instance, empirical and experimental evidences of toughening point to a coupling between elastic and fracture properties of heterogeneous materials, which contradicts some mathematical results. In this talk, I will present an attempt at formalizing a concept of effective toughness, to compute it, and to design materials with extreme fracture properties.[-]