## 6 Conclusions and Perspectives  
In this review, we appraised the facet-dependent reactivity of ceria nanoparticles, on the ground of ceria-based transition metal catalysts. Through the morphological control of ceria nanoparticles (e.g., rods, cubes, and polyhedra), the concept of \"shape engineering\" can be employed to obtain reliable structure-performance relationships, which in turn could provide the basis for the rational design and fabrication of cost-efficient and highly-active catalyst formulations. By means of a complementary characterization study, the morphological effects of ceria on key activity descriptors were initially explored. It was revealed that ceria nanoparticles with a rod shape possess excellent redox properties, related to their abundance in oxygen vacancies and weakly bound labile oxygen species. In particular, the following trend in relation to oxygen storage capacity (OSC) was obtained for bare ceria nanoparticles: rods > polyhedra > cubes, well correlated with the energy formation of anionic vacancies, i.e., \(\{111\}\) > \(\{100\}\) > \(\{110\}\). More importantly, it was clearly revealed that the incorporation of different transition metals (e.g., Cu, Fe, Ni, and Co) to ceria nanoparticles considerably accelerates surface oxygen reduction via metal-support interactions, following, however, the identical trend obtained for bare ceria nanoparticles. The latter clearly demonstrates the pivotal role of ceria morphology toward determining the redox features of ceria-based mixed oxides. Figure 14: Methane Yield (defined as CO\({}_{2}\) conversion x selectivity to CH\({}_{4}\)) for CeO\({}_{2}\)-NR, commercial ceria (CeO\({}_{2}\)-Com) and the corresponding Ni-based samples. Reaction conditions: Weight Hourly Space Velocity = 30,000 mL g\({}^{-1}\) h\({}^{-1}\), H\({}_{2}\):CO\({}_{2}\) = 4:1, P = 1 atm [39]. For reactions obeying a redox-type mechanism, where the redox cycle between labile and molecular oxygen mainly determines the reaction rate, perfect quantitative relationships between catalytic performance--redox properties--and ceria morphology were disclosed. From the practical perspective, extremely active composites were developed by concurrently adjusting the shape and composition of ceria-based mixed oxides. For instance, Cu/CeO\({}_{2}\)-nanorods exhibit full CO conversion at ca. 100 \({}^{\circ}\)C, surpassing by far the CO oxidation ability of a typical oxidation catalyst, such as Pt/Al\({}_{2}\)O\({}_{3}\). In a similar manner, extremely active composites for CO\({}_{2}\) methanation were synthesized by combining Ni with CeO\({}_{2}\) nanorods. Besides the alteration of solid state properties by the manipulation of shape at nanoscale, the fine adjustment of electronic state (e.g., by alkali promotion) can provide an additional powerful tool towards regulating the chemisorption properties and consequently the reactivity of metal oxides. Hence, the modulation of electronic state, size and shape at the nanoscale could provide the design direction on the way to fabricate cost-efficient earth-abundant metal-oxide catalysts for several environmental and energy processes. In this direction, the development of facile and versatile synthesis routes towards the precise control of shape and size at nanoscale is of paramount importance. Moreover, the shape engineering of reducible carriers, such as ceria, could provide a powerful tool in order to rationally design and develop single atom supported catalysts with the anticipated activity and stability. The fine-tuning of the single metal atoms-support interaction through metal anchoring on specific crystal planes, could lead to interfacial sites of exceptional activity and stability. Furthermore, it should be mentioned that the development of composite systems, through the combination of reducible oxide supports with bimetallic or carbide-based materials could lead to multifunctional composites with enhanced properties and catalytic performance.