This paper establishes a theoretical approach to determining the random packing fraction for both close and loose packing of spheres, and is therefore pertinent to both granular materials studies and to the more traditional use of such results in the theory of liquids. It also contains a fairly extensive survey of the prior literature. I think it is for the latter reason that this paper has been cited a lot, and is probably my most cited paper, having 135 citations so far through 1997.