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This thesis sums up the research work I performed as a PhD student inSapienza Universit\`a di Roma, and \'Ecole Normale Sup\'erieure, Paris, underthe joint supervision of Prof. Giorgio Parisi and Dr. Francesco Zamponi. Thethesis focuses on the theoretical study of metastable glasses prepared throughnon-equilibrium protocols. The first two chapters contain a review of thephenomenology of equilibrium supercooled liquids and non-equilibrium glasses,along with an exposition of the theoretical tools used up to now to approachthe glass problem; the third chapter contains a review of the theoretical toolswhich are employed in the following of the thesis; the following two chapterscontain our main result, namely a mean-field and first-principles theory ofmetastable glassy states which, as we show, is both able to reproduce knownobservations and to formulate new predictions and insights into the very natureof the glass phase, with tangible consequences in terms of behavior at highdensities (or equivalently, low temperatures) and elasto-plastic response understrain; the last two chapters contain a numerical check of some of the results,and our conclusions and proposals for further research. The results I report inthe present work have been for the most part already published, but here theyare presented in a consistent and (as much as possible) self-contained manner.

Following the evolution of metastable glassy states under external perturbations: compression and shear-strain