The main current theories dealing with the crystalline structures of the fluorite related rare earth oxides, including those corresponding to reduced oxides, one based on the distribution of the coordination defect inside the fluorite structure, and the other which proposes the establishment of modular sequences constituted by modules with fluorite structure, are presented and comparatively explored in detail. Our in-depth analysis of both approximations indicates that they in fact provide smart and efficient rationalizations of the currently known intermediate rare earth oxides structures. We prove however that the strict application of the principles and rules proposed by each theory does not yield unique and unambiguous results for most of the members of the homologous series, as it has been claimed up to now. Moreover, the controversy about the reliability of these two, apparently different and competing, theories is definitely clarified and the exact equivalence of their structural predictions is demonstrated. Finally, we propose new extra systematization rules, not considered up to now in neither of these theoretical approaches, to overcome the observed limitations to properly rationalize the structure of this so technologically important family of oxides. (C) 2011 Elsevier B.V. All rights reserved.