Everyday life tells us that matter acquires rigidity when it cools down - lava flows turn into solid rocks - or when it is compacted - remember kids packing down the sand to build up castles on the sea shore. As suggested by these examples, this is not only the case for materials, which crystallize at low temperature or high pressure. It also happens for disordered media such as foams, emulsions, colloidal suspensions, granular media and glasses.
In 1998 Liu and Nagel presented a (Temperature-Stress- Density) phase diagram, the so-called "Jamming diagram", the purpose of which was to encompass in a unique framework the glass transition and the emergence of yield stress, two challenging issues in modern condensed matter physics.
In this talk, I will review what, 20 years later, we have learnt about elementary excitations and relaxation processes in glasses using model experiments with vibrated granular media. More specifically, I will (i) discuss differences and connections between the glass and the jamming transition, (ii) illustrate the type of hierarchical dynamics, which control granular glass relaxation and (iii) present very recent results about a glass to glass transition, the so called Gardner transition, of which we obtained recently the first experimental evidence.