Nanostructured materials based on ceria (CeO2) and Pt have a wide range of applications in catalysis, such as in the three-way conversion in automobile exhausts, in anode or cathode 3 materials of fuel cells, or for mediating the water gas shift reaction, among others. CeO2 is typically used in such materials as a non-inert support for the more active Pt phase, leading to intricate metal-support interactions that affect the electronic structure and chemical properties of both the metal and the oxide. These electronic metal-support interactions further complicate the already challenging task of characterizing the properties of nanostructured catalytic materials, which are typically structurally complex. Their size, structure, and oxidation state not only depend on preparation conditions, but also often undergo significant transformations under reaction conditions, as revealed by in situ or operando spectroscopic techniques. These structural and environmental complexities therefore hinder the straightforward computational modelling of working heterogeneous catalysts by means of first principlesbased approaches. For systems based on Pt and ceria, Pt can be found in the form of nano-or subnanoparticles of varying size, or as single atoms either anchored to the ceria surface or inserted in the ceria lattice. Atomically dispersed Pt on ceria substrates has been studied extensively by means of combined experiment and computational approaches during the last decade because they allow to significantly increase specific activity for different reactions. In such composites, Pt is often found in cationic form (i.e. Pt n+ species with n= 1, 2, or 4) either occupying Ce positions of the ceria lattice or deposited on undercoordinated sites of ceria substrates. The oxidation state of Pt atoms depends on their coordination environment and on the stoichiometry of ceria substrate, which can either accept or donate electrons by varying the occupation of the Ce4f states (reducing Ce 4+ cations to Ce 3+ and vice versa) and/or the amount of O in the ceria lattice.