The Jamming Transition and the Marginally Stable Solid

We review the physics of jamming from the theoretical, experimental and numerical perspectives. We summarize the mean-field theory of jamming and the marginally stable solid phase, with particular emphasis on the connection with the Replica Symmetry Breaking theory of glasses. We report validations of the mean-field theory of jamming from experimental and numerical studies of critical behaviors near the transition. In particular, we describe the physics of jamming of frictionless, spherical particles, as well as more recent work on jamming of frictionless, non-spherical particles and frictional, nearly spherical particles. We also present current efforts in expanding the mean-field theory to systems that more closely resemble externally driven granular media, cell aggregates, and active colloidal suspensions.