Jamming is a prototypical mechanism for rigidity formation. As the geometrical constraints between particles become important, a fluid can lose its ability to flow. Can we learn anything about the process of rigidity formation in molecular fluids by studying flowing granular matter where jamming is readily visible? Does a solid formed by crossing the jamming transition behave in the same way as do ordinary solids? We have been studying the jamming transition using computer simulations. We find that the properties of the marginally-jammed solid are indeed unusual and provide a new way of thinking about disordered systems generally. I will give an overview of the properties of the marginally-jammed solid, concentrating on the normal-mode excitations and how they control the physical properties of the solid at low temperatures.