Three-way catalysis (TWC) involves simultaneous removal of the three pollutants (i.e., CO, NOx, and HCs) which led to the branch of auto-exhaust catalysis. CeO2 has become the main component of TWC catalyst because of its oxygen storage storage (OSC) property to supply oxygen under excess fuel condition and store oxygen under lean condition. Substitution of smaller isovalent cations like Ti4+, Zr4+ and Hf4+ ions in CeO2 forming Ce1-xMxO2 (M = Ti, Zr &Hf) solid solution enhance the OSC property. XRD along with EXAFS study showed that cations arrange in FCC lattice but oxygen coordination around metal ions is split into 4 + 4 coordination in Ce1-xMxO2 instead of ideal 8 coordination in CeO2. The longer Ce/Ti/Zr – O bonds are weakly bound and can be easily removed by H2 giving high OSC value than pure CeO2. Among the three OSC systems studied here, Ce0.5Zr0.5O2 showed exceptionally high OSC which lead to formation of a new a pyrochlore, Ce2Zr2O6.3. This compound is nearly metallic. Ce0.85-xTi0.15PtxO2- (x = 0.01 & 0.02) crystallizes in fluorite structure and Pt is ionically substituted with 2+ and 4+ oxidation states. H/Pt atomic ratio at 30 oC over Ce0.84Ti0.15Pt0.01O2- is 5 and over Ce0.99Pt0.01O2-δ is 4 against just 0.078 for 8 nm Pt metal particles. Carbon monoxide and hydrocarbon oxidation activity are much higher over Ce1-x-yTixPtyO2 (x= 0.15, y= 0.01, 0.02) compared to Ce1-xPtxO2 (x= 0.01, 0.02). Synergistic involvement of Pt2+/Pt0 and Ti4+/Ti3+ redox couples in addition to Ce4+/Ce3+ due to the overlap of Pt(5d), Ti(3d), and Ce(4f) bands near EF is shown to be responsible for enhanced redox property and higher catalytic activity. On substitution of Pd ion in Ce1-xTixO2, more lattice oxygen is found to be more labile than Pd in CeO2. The easy removal of oxygen from the more reducible Ti4+ containing support plays a major role in showing higher catalytic activity of this material for CO oxidation, N2O and NO reduction by CO. The catalyst shows 100% N2 selectivity  240 oC in NO+CO reaction. It has been shown that oxide ion vacancy creation created by removal of lattice oxygen by CO is responsible for dissociation of NO or N2O at a lower temperature. Ionicity of Pd2+ ion in different support could be varied by varying the ionicity of the oxide support itself. Rates of CO oxidation increases or activation energy decreases over Ce1-xPdxO2-δ, Ti1-xPdxO2-δ and Ce1-x-yMxPdyO2-δ (M = Ti, Zr, Hf ; x = 0.25, 0.4 ; y = 0.02) is increased with ionicity of Pd2+ ion. The substitution of Sn in CeO2 forming Ce1-xSnxO2 (x = 0.1-0.5) solid solution was prepared using tin oxalate precursor by solution combustion method. These oxides can be promising support for noble metals because of the Sn4+  Sn2+ redox couple in addition to Ce3+/Ce4+. The two electron process involved in the redox reaction of Sn as well as easy reducibility of Sn4+ to Sn2+ offers a far better redox catalytic system hitherto not reported. Ce1-xSnxO2 solid solutions as well as Pd ion substituted Ce1-xSnxO2 was prepared for the first time.