Atomistic simulations reveal that the chemical reactivity of ceria nanorods is increased when tensioned and reduced when compressed promising strain-tunable reactivity; the reactivity is determined by calculating the energy required to oxidize CO to CO2 by extracting oxygen from the surface of the nanorod. Visual reactivity “fingerprints”, where surface oxygens are colored according to calculated chemical reactivity, are presented for ceria nanomaterials including: nanoparticles, nanorods, and mesoporous architectures. The images reveal directly how the nanoarchitecture (size, shape, channel curvature, morphology) and microstructure (dislocations, grain-boundaries) influences chemical reactivity. We show the generality of the approach, and its relevance to a variety of important processes and applications, by using the method to help understand: TiO2 nanoparticles (photocatalysis), mesoporous ZnS (semiconductor band gap engineering), MgO (catalysis), CeO2/YSZ interfaces (strained thin films; solid oxide fuel cells/nanoionics), and Li-MnO2 (lithiation induced strain; energy storage).