Abstract：
　　Despite extensive studies of transition-metal particles (Pt, Au, etc) supported on cerium oxides, CeO₂, surfaces, e.g., CeO₂(111), fundamental issues such as the role of the TM-O interactions in the oxidation state change of the Ce atoms are still in debate. In this talk, I will revise and discuss few contributions from our group based on density functional theory calculations for TM clusters (TM₄, TM₁₃, TM = Zr, Pd, Ag, Pt, Au, etc) supported on CeO₂(111). Furthermore, we will discuss future perspectives by exploring the combination of finite-size ceria particles and transition-metal clusters.