  Amorphous materials as diverse as foams, emulsions, colloidal suspensions and
granular media can jam into a rigid, disordered state where they withstand
finite shear stresses before yielding. Here we review the current understanding
of the transition to jamming and the nature of the jammed state for disordered
packings of particles that act through repulsive contact interactions and are
at zero temperature and zero shear stress. We first discuss the breakdown of
affine assumptions that underlies the rich mechanics near jamming. We then
extensively discuss jamming of frictionless soft spheres. At the jamming point,
these systems are marginally stable (isostatic) in the sense of constraint
counting, and many geometric and mechanical properties scale with distance to
this jamming point. Finally we discuss current explorations of jamming of
frictional and non-spherical (ellipsoidal) particles. Both friction and
asphericity tune the contact number at jamming away from the isostatic limit,
but in opposite directions. This allows one to disentangle distance to jamming
and distance to isostaticity. The picture that emerges is that most quantities
are governed by the contact number and scale with distance to isostaticity,
while the contact number itself scales with distance to jamming.
