The volume fraction phi for random close packed (RCP) spheres is approximately 0.64.  It is well known that higher RCP volume fractions are achieved by using collections of particles with a variety of sizes. The variety of sizes is often quantified by the polydispersity of the particle size distribution: the standard deviation of the radius divided by the mean radius.  I’ll show that for 2D and 3D packings, the skewness also plays an important role (related to the third moment of the size distribution).  I will also discuss some of our work on random close packing in confined spaces.