A chemical mechanical polishing (CMP) mechanism of a glass surface by a CeO₂ abrasive grain under water environment has not been elucidated because the CMP process is complicated combination of chemical reactions and mechanical polishing. In this review, we introduce our successful clarification of the CMP mechanism by computational simulation methods. First, we revealed that the oxygen defects in the CeO₂ abrasive grains lead to the generation of exposed Ce³⁺ atoms on the CeO₂ surface and then the chemical reactions of the exposed Ce³⁺ atom and the glass surface make the elongation of Si-O bonds. We also clarified that H₂O molecules react with the above elongated Si-O bonds and then the Si-O bonds are dissociated. These chemical reactions are suggested to soften the glass surface and enhance the mechanical polishing. Furthermore, according to the above clarified CMP mechanism, we succeeded to propose the design principles for the alternative materials of CeO₂ abrasive grains.