Monolayers of rare gas atoms adsorbed onto the basal planes of graphite play the same prototype role in two dimensions that rare gas liquids and solids do in three dimensions. In recent experiments such novel phenomena as continuous melting, the lack of true crystallinity in two dimensions, orientationally ordered fluid phases, and melting from a solid to a reentrant fluid with decreasing temperature have been observed. Because the forces in these rare gas monolayers are simple and well understood, by studying them the investigator can examine a direct interface between experiment and first principles. In order to understand the phases and phase transitions that occur in such materials, it is necessary to consider the geometrical matching of the rare gas overlayer to the graphite substrate. It turns out that in two dimensions both the local and the long-distance behavior are important. These two-dimensional rare gas solids may be effectively probed with synchrotron x-ray techniques, and the results of a series of synchrotron x-ray scattering studies of these solids are presented.