The present work focuses on two fluorite-structured groups of materials: the hydrides of the rare earths (and actinides) and several specific metal oxides, and is authored by researchers among the most competent and active in the field. By contrast to the classical "historic" alkaline-earth halides, non-stoichiometry appears as a key issue for both groups treated here. The former group has attracted particularly close attention because of its possible candidature as hydrogen storage material within the vast prospect of the clean energy economy. In addition, the amazing property of transiting from the metallic to the semiconducting state and back by simply changing the hydrogen concentration between dihydride and trihydride had led to the development of the so-called "switchable mirrors" evolving between the opaque or the reflecting and optically transparent.