Jamming and glass transitions are two phenomena whose mutual relation is not quite clear. The `jamming transition’ happens when a system of, say, hard frictionless spheres is rapidly compressed and reaches an infinite pressure point. This point is characterised by a diverging length and soft modes, just as a critical phenomenon. At the bottom of this criticality is the fact that when the system jams it does so under globally isostatic mechanical equilibrium. On the other hand, the glass transition is also characterised by diverging dynamic (and presumably also static) lengths. It may happen at finite temperatures and pressures, and for soft potentials. The question as to what, if any, is the relation between the two transitions has been difficult to answer due to a lack of situations where both sets of theories apply simultaneously. I shall discuss a family of models that does precisely that : it possesses on the one hand a jamming transition with diverging lengths and soft modes, and on the other an ideal glass transition.