In situ X-ray and neutron diffraction experiments at high temperatures were performed to monitor the lattice response due to conversions between the Ce4+ and Ce3+ in CeO2-based oxide catalysts, CeO2, Ce1-xLaxO2-x/2 and Ce1-xZrxO2 with and without impregnation of Pt metal. The significant difference in the Ce4+ and Ce3+ ionic radius permitted a quantitative measurements of the fraction of Ce3+ in the cubic phases of crystalline CeO2 and the oxide solid solutions during the redox cycle. The reduction kinetics, kt={1-(1-x)(1/3))}(2) (x=fraction of Ce3+, t-time, k=constant) for CeO2 and Ce1-xLaxO2-x/2 were characterized from an analysis of the X-ray data collected under a CO/N-2 atmosphere at 500-700 degrees C. Pt-impregnated Ce0.1Zr0.9O2 was examined by neutron diffraction measurements under both CO/Ar and O-2/Ar atmospheres up to similar to 700 degrees C. Under a CO/Ar atmosphere, Pt-impregnation accelerates the reduction of Ce4+ to Ce3+ first on the interface of the metal and oxide particles, generating oxygen vacancies and releasing CO2 molecules. Subsequently, oxygen vacancies migrate to the bulk of the oxide particles. The significance of the redox behavior of CeO2 in automotive three-way catalysts for purification of exhaust pollutants is discussed.