Nanozymes were introduced approximately 15 years ago as inorganic materials capable of mimicking the catalytic abilities of natural (protein-based) enzymes. While the catalytic efficiency of nanozymes typically does not match that of enzymes, their research gains special attention due to their potential advantages over conventional enzymes, particularly their higher resistance to adverse conditions. This article focuses on the utilization of cerium oxide for the catalytic acceleration of non-redox reactions (e.g., dephosphorylation). It elucidates certain analogies between the functioning of conventional enzymes (metalloenzymes) and the nanozymatic activity of ceria, and the distinctions in the mechanisms of action between the two catalyst types. The unique catalytic (enzymatic) ability of cerium oxide is predetermined by the fine interplay between surface reactivity (associated with surface defects) and structural integrity (simplicity and stability of the subsurface crystalline structure). Limitations associated with the less flexible nature of cerium oxide are discussed, together with strategies to overcome them, which are based on the new concept of the dynamic active site. Possible generalizations to other metal oxide-based nanozymes are briefly mentioned.