The physics of disordered media, from metallic glasses to colloidal
suspensions, granular matter and biological tissues, offers difficult
challenges because it often occurs far from equilibrium, in materials lacking
symmetries and evolving through complex energy landscapes. Here, we review
recent theoretical efforts to provide microscopic insights into the mechanical
properties of amorphous media using approaches from statistical mechanics as
unifying frameworks. We cover both the initial regime corresponding to small
deformations, and the yielding transition marking a change between elastic
response and plastic flow. We discuss the specific features arising for systems
evolving near a jamming transition, and extend our discussion to recent studies
of the rheology of dense biological and active materials.Comment: 20 pages, 7 figure