Armed with the proper background, we are now ready to describe models that have been put forward to explain the build-up of interstitial electron density in HPEs. Ideally, such a model would be able to predict the electronic structure of an element or compound as a function of pressure, including the conditions at which it deviates from expectations based upon TFD theory (Figure ). As we will see below, none of the models proposed to date can fulfill this aspiration, though progress has been made on developing an understanding of the factors driving electron localization.