The ability of copper proteins to process dioxygen at ambient conditions has inspired numerous research groups to study their structural, spectroscopic and catalytic properties. Catechol oxidase is a type-3 copper enzyme usually encountered in plant tissues and in some insects and crustaceans. It catalyzes the conversion of a large number of catechols into the respective o-benzoquinones, which subsequently auto-polymerize, resulting in the formation of melanin, a dark pigment thought to protect a damaged tissue from pathogens. After the report of the X-ray crystal structure of catechol oxidase a few years earlier, a large number of publications devoted to the biomimetic modeling of its active site appeared in the literature. This critical review (citing 114 references) extensively discusses the synthetic models of this enzyme, with a particular emphasis on the different approaches used in the literature to study the mechanism of the catalytic oxidation of the substrate (catechol) by these compounds. These are the studies on the substrate binding to the model complexes, the structure-activity relationship, the kinetic studies of the catalytic oxidation of the substrate and finally the substrate interaction with (per)oxo-dicopper adducts. The general overview of the recognized types of copper proteins and the detailed description of the crystal structure of catechol oxidase, as well as the proposed mechanisms of the enzymatic cycle are also presented.