  Packings of identical objects have fascinated both scientists and laymen
alike for centuries, in particular the sphere packings and the packings of
identical regular tetrahedra. Mathematicians have tried for centuries to
determine the densest packings; Crystallographers and chemists have been
fascinated by the lattice packings for centuries as well. On the other hand,
physicists, geologists, material scientists and engineers have been challenged
by the mysterious random packings for decades. Experiments have shown the
existence of the dense random sphere packings and the loose random sphere
packings for more than half a century. However, a rigorous definition for them
is still missing. The purpose of this paper is to review the random solid
packings and to create a mathematical theory for it.
