The non-equilibrium transition from a fluid–like state to a disordered solid–like state, known as Jamming, occurs in a wide variety of physical systems as diverse as simple liquids, colloidal suspensions, molecular fluids, foams and granular material by varying the control parameters. A part of my research work was devoted to the case of glass-former liquids. When a liquid is cooled fast enough avoiding crystallization, its relaxation time increases by many orders of magnitude, and overcomes any experimentally available time-scale: then we get a glass. The slowing down has been related to the presence of Dynamical Heterogeneities, i.e. clusters of particles dynamically correlated during time and over length, whose typical size grows on approaching the glassy phase. In this context, I have investigated via Monte Carlo simulations a popular glass former model. I find that, contrary to current expectations, the relaxation process and the dynamical heterogeneities are characterized by different time scales. This implies that they have a distinct physical origin. Indeed, I show that the relaxation time is related to a reverse percolation transition, whereas the time of maximum heterogeneity is related to the spatial correlation between particles, one can rationalized using theories for diffusing defects. This investigation leads to a geometrical interpretation of the relaxation process of glassy systems, and of the different observed time scales. Another part of my work focuses on the Jamming of non-thermal systems. In particular, I have investigated the case of frictional Granular materials via molecular dynamics simulations, reporting the existence of new rheological regimes, which are conveniently described in a jamming phase diagram with axes density, shear stress, and friction coefficient. The resulting jammed states are characterized by different mechanical and structural properties and appear not to be `fragile' as speculated. In particular, I find a regime, characterized by extremely long processes, with a diverging timescale, whereby a suspension first flows but then suddenly jams. I have related this sudden jamming transition to the presence of impeded dilatancy.