Heterogeneities in amorphous systems under shear

Chapter of "Dynamical Heterogeneities in glasses, colloids and granular materials", Eds.: L. Berthier, G. Biroli, J-P Bouchaud, L. Cipelletti and W. van Saarloos (Oxford University Press, to appear), more info at http://w3.lcvn.univ-montp2.fr/~lucacip/DH_book.htmThe last decade has seen major progresses in studies of elementary mechanisms of deformation in amorphous materials. Here, we start with a review of physically-based theories of plasticity, going back to the identification of ``shear-transformations'' as early as the 70's. We show how constructive criticism of the theoretical models permits to formulate questions concerning the role of structural disorder, mechanical noise, and long-ranged elastic interactions. These questions provide the necessary context to understand what has motivated recent numerical studies. We then summarize their results, show why they had to focus on athermal systems, and point out the outstanding questions