A method of making a structured, doped, cerium oxide nanoparticle includes (a) forming a first reaction mixture including cerium(III), an optional metal ion other than cerium, a base, a stabilizer, and a solvent, (b) contacting the first reaction mixture with an oxidant, (c) forming a cerium oxide nanoparticle core by heating the product of step (b), (d) forming a second reaction mixture by combining with the first reaction mixture one or more metal ions other than cerium, and an optional additional quantity of cerium(III), and (e) forming a shell surrounding the core of cerium oxide by heating the second reaction mixture to produce a product dispersion of structured cerium oxide nanoparticles.