Since their first development in the 1960s, phase change (PC) memory materials have become essential components of optical memories (DVD-RW, Blu-ray Disc, …) used in countless households worldwide. They are now poised to play a decisive role in future non-volatile computer memories. PC memory materials are restricted to those with an extremely rapid and reversible transition between the amorphous and crystalline phases of an appropriate recording medium, and their development and optimization has been hindered by the inherent difficulties in determining amorphous structures. Alloys of germanium, antimony, and tellurium (“GST” alloys) are among the most widely used in the above contexts, and there has been much speculation concerning their amorphous structures. Theoreticians were slow to appreciate the rich array of problems awaiting their attention, but the past few years have seen a dramatic change in this situation. Density functional (DF) calculations, which are generally free of adjustable parameters, have now been reported on numerous systems. We review here the information that has resulted about the amorphous structures of GST-alloys.