  The deformation and flow of disordered solids, such as metallic glasses and
concentrated emulsions, involves swift localized rearrangements of particles
that induce a long-range deformation field. To describe these heterogeneous
processes, elastoplastic models handle the material as a collection of
'mesoscopic' blocks alternating between an elastic behavior and plastic
relaxation, when they are too loaded. Plastic relaxation events redistribute
stresses in the system in a very anisotropic way. We review not only the
physical insight provided by these models into practical issues such as strain
localization, creep and steady-state rheology, but also the fundamental
questions that they address with respect to criticality at the yielding point
and the statistics of avalanches of plastic events. Furthermore, we discuss
connections with concurrent mean-field approaches and with related problems
such as the plasticity of crystals and the depinning of an elastic line.
