Syntheses: Mechanical properties of heterogeneous media: Which material for which model? Which model for which material?

This paper aims to provide an overview of observed situations in heterogeneous materials, both in terms of the geometry of the multiphase structure (topology, shapes and scales) and in terms of the mechanical contrast between the constituents. An overview of some tools available in micromechanics will be given in order to answer the following two questions: What is the best model class for a given material? What is the best model material to test a mechanical theory? Some remarks which probably require new conceptual approaches will be outlined in the conclusion.