In the present micro-review, we describe the Cu(II) binding to several forms of amyloid-β peptides, the peptides involved in Alzheimer's disease. It has indeed been shown that in addition to the "full-length" peptide originating from the precursor protein after cleavage at position 1, several other shorter peptides do exist in large proportion and may be involved in the disease as well. Cu(II) binding to amyloid-β peptides is one of the key interactions that impact both the aggregating properties of the amyloid peptides and the Reactive Oxygen Species (ROS) production, two events linked to the etiology of the disease. Binding sites and affinity are described in correlation with Cu(II) induced ROS formation and Cu(II) altered aggregation, for amyloid peptides starting at position 1, 3, 4, 11 and for the corresponding pyroglutamate forms when they could be obtained (i.e. for peptides cleaved at positions 3 and 11). It appears that the current paradigm which points out a toxic role of the Cu(II) - amyloid-β interaction might well be shifted towards a possible protective role when the peptides considered are the N-terminally truncated ones.