Synthetic copper-dioxygen complex design, generation and characterization, play a crucial role in elucidating the structure/function of copper-based metalloenzymes, including dopamine β-monooxygenase, lytic polysaccharide monooxygenases, particulate methane monooxygenase, tyrosinase, hemocyanin, and catechol oxidase. Designing suitable ligands to closely mimic the variable active sites found in these enzymes poses a challenging task for synthetic bioinorganic chemists. In this review, we have highlighted a few representative ligand systems capable of stabilizing various copper-dioxygen species such as CuII-(O2 •-)(superoxide), Cu2 II-(μ-η 1:η 1-O2 2-) (trans/cis-peroxide), Cu2 II-(μ-η 2:η 2-O2 2-)(side-on peroxide) and Cun II--OOH (hydroperoxide) species. Here, we discuss the ligand type utilized, syntheses, and spectroscopic characterization of these species. We also delineate reactivity patterns, particularly electrophilic arene hydroxylation by a side-on peroxo species which occurs via a "NIH shift" mechanism and thermodynamic-kinetic relationships among Cu2-(O2 •-)/O2 2-/-OOH moieties.