We have proposed that the glass transition is one example of a broader class of jamming transitions, where systems can develop extremely long stress relaxation times in disordered states as temperature is lowered, an applied shear stress is lowered, or particle density is raised. Other jamming systems include colloidal suspensions, foams and granular materials. We suggested that the state of a jamming system might be represented by a “jamming phase diagram” as a function of temperature, shear stress and density. Such a diagram is unconventional because the glass transition and other jamming transitions are not sharp; for example, the glass transition temperature depends on how long one is willing to wait in order to measure the stress relaxation time. Nevertheless, there appears to be a point (Point J) on the diagram where the jamming transition is truly sharp. This point represents the onset of jamming with increasing particle density at zero temperature, and it lies near the density commonly called random close-packing. Our numerical simulations suggest that this point has characteristics of both first and second-order phase transitions. I will show that aspects of this transition can be understood by analogy to a correlated percolation model that can be solved exactly in the mean-field limit.