I will discuss progress in two ongoing sets of experiments on the packing of macroscopic objects. The first of these is a neglected aspect of the old problem of packing identical spheres. Much attention has recently been paid to packings of frictionless spheres, particularly to the geometry and mechanics of the random close packed state. I will report new results on the opposite limit: that of the loosest mechanically stable packings achievable in systems of frictional spheres. The second class of packing problems I will discuss is the packing of a thin sheet in a volume of much smaller linear dimension. We probe the interior of this crumpled object by x-ray microtomography and find that the geometry is in many respects isotropic and homogeneous. Furthermore, local nematic order appears to emerge during the crumpling process.