Peptides and proteins with N-terminal amino acid sequences NH -Xxx-His (XH) and NH -Xxx-Zzz-His (XZH) form well-established high-affinity Cu -complexes. Key examples are Asp-Ala-His (in serum albumin) and Gly-His-Lys, the wound healing factor. This opens a straightforward way to add a high-affinity Cu -binding site to almost any peptide or protein, by chemical or recombinant approaches. Thus, these motifs, NH -Xxx-Zzz-His in particular, have been used to equip peptides and proteins with a multitude of functions based on the redox activity of Cu, including nuclease, protease, glycosidase, or oxygen activation properties, useful in anticancer or antimicrobial drugs. More recent research suggests novel biological functions, mainly based on the redox inertness of Cu in XZH, like PET imaging (with Cu), chelation therapies (for instance in Alzheimer's disease and other types of neurodegeneration), antioxidant units, Cu transporters and activation of biological functions by strong Cu binding. This Review gives an overview of the chemical properties of Cu-XH and -XZH motifs and discusses the pros and cons of the vastly different biological applications, and how they could be improved depending on the application.