Amorphous systems form a large fraction of the solid materials that surround us, from polymer glasses to mineral or metallic glasses, from toothpaste (a colloidal paste) to granular materials. Still, a theoretical framework for describing the mechanical properties of such materials, comparable to the dislocation theory that describes crystalline systems, is still missing. Our understanding of prominent experimental feature such as the heterogeneous character of deformation, or the temperature and rate dependence of the mechanical response, is very limited.These materials indeed combine several difficulties. In contrast to liquids or crystals, they are intrinsically out of equilibrium, and their microstructure presents a large statistical distribution of mechanically distinct local environments. The importance of the notion of heterogeneity in the mechanical behaviour of amorphous systems is being increasingly recognized, still there is no numerical or theoretical model that incorporates this microscopic feature into a macroscopic description of deformation and flow.The aim of the proposed research program is to build such models, within a multiscale approach seeking inspiration from dislocation dynamics, from the statistical physics of glasses and from the physics of dynamical critical phenomena. The proposed approach is based on a combination of intensive numerical simulations at the atomic scale and at a coarse grained scale, which will necessitate the development of efficient numerical schemes. The statistical analysis will allow us to understand the universal and non universal features of material behaviour in terms of the interactions between the atomic constituents, and to establish the validity and importance of new concepts such as mechanical activation or dynamical heterogeneities.