Abstract: | Abstract: In this colloquium I will review recent progress in understanding the mechanical responses of amorphous solids to external strains. Fundamental plastic instabilities appear as saddle-node bifurcations which result in eigenvalues of the system's Hessian matrix hitting zero, leading to either local or highly correlated non affine irreversible re-arrangements of particle positions. The theory results in a consistent statistical mechanics of plasticity in amorphous solids, including ab-initio predictions of the yield-stress and of important rheological laws. |