What characterizes a solid is its way to respond to external stresses. Ordered solids, such crystals, display an elastic regime followed by a plastic one, both well understood microscopically in terms of lattice distortion and dislocations. This paradigm hardly applies to amorphous solids at low temperatures where elasticity appears to be always mixed with plasticity and avalanches resulting in a very jerky behavior. \par In this talk I will show that in a very large class of amorphous solids this behavior emerges upon cooling at a new critical point, the Gardner transition. Here the elastic response completely breaks down due to the appearance of a lot of very soft and nontrivial low energy excitations. The nonlinear elastic susceptibilities diverge and the response of the system to a deformation becomes history and time dependent. This picture characterizes the whole low temperature phase thus making possible the identification of a new kind of solid phase: the marginal glass. I will show how the Gardner transition and the marginal phase are precursors of the yielding point where mechanical failure occurs after that a sufficiently strong deformation is applied. I will also argue how these findings could clarify the true nature of the yielding transition in amorphous systems. Finally I will show how the marginal phase provides an explanation of the long standing puzzle of the boson peak in amorphous solids.