Unlike liquids or crystals, amorphous solids (aka glasses) are generally out-of-equilibrium. It is highly debated on the nature, and sometimes even the existence, of the phase transitions in such non-equilibrium systems. In this talk, I will briefly review some recent progress in the research of three transitions: (i) the liquid to glass transition, (ii) the jamming transition which marks the onset of rigidity in particulate systems, and (iii) the Gardner transition which separates the stable glasses produced at the glass transition from the marginally stable glasses at low temperatures. Remarkably, these three phase transitions are unified within a common framework by a mean-field theory that is exact in infinite dimensions. I will also discuss about the numerical effort that has been made to examine the theoretical predictions in physical dimensions.