Ceria is an important material for chemical conversion processes in catalysis. Its intrinsic properties as a reducible oxide can be exploited to achieve catalytic selectivity and activity. However, numerous phenomenological characteristics of ceria remain unknown and its active nature is ever slowly being unraveled. Well defined models of ceria (111) are an important way to systematically study these properties and take advantage of new in situ methods that require pristine materials that allow for the interrogation of the most fundamental traits of this material. The ceria-Ru(0001) model is now the most well studied model surface with numerous aspects of its preparation, atomic structure and reactivity studied by several groups. The preparation of CeOx structures oriented with a (111) surface termination can be achieved through molecular beam deposition, facilitating the growth of well-defined nanostructures, microparticles, and films on the Ru(0001) surface. The growth mechanism exploits the epitaxial relationship between CeOx and Ru to form a carpet mode of well oriented layers of O-Ce-O. These models can be studied to unravel the atomic structure and the oxidation state (Ce-4* and Ce3+), as prepared and under redox conditions (reduction/oxidation) or with reaction using reactants (e.g, H-2, methanol). Here, we present a discussion of these most recent observations pertaining to the growth mode, arrangement of atoms on the surface, characteristic chemical state, and redox chemistry of the CeOx-Ru surface. With insights from these studies we propose new strategies to further unravel the chemistry of ceria. (C) 2016 Elsevier B.V. All rights reserved.