In the present perspective, we give a critical review on the coordination chemistry of the metal ions copper and zinc to the amyloid-β (Aβ) peptide; such complexes have been linked to Alzheimer's disease. We focus on two main issues: the identification of the coordination sphere of the Cu(II) and Zn(II) ions and the affinity of these metal ions towards the peptide. With the aim to come up with as few as possible valuable structural models and binding affinity values, we critically review the divergent propositions reported in the literature and take into account the experimental differences and the limits of the methods used in the published studies. We propose that: (i) the conditional dissociation constant of the Cu(Aβ) complexes lies in the range of 10 pM to 100 nM, with a preference for the region between 100 pM to 1 nM. (ii) Two most likely coordination modes for the predominant form of the Cu(Aβ) complexes at physiological pH can be retained, both being 3N1O distorted square planar. In the first model, the Cu(II) ion is coordinated by the Nτ atoms of the three His residues and the carboxylate of the Asp1. In the second model, both the N-terminus and the carboxylate functions of Asp1 are ligated together with the Nτ of His6 and of His13 (or His14). An equilibrium between these two forms at room temperature, and a preferentially freezing out of the second one would explain most of the divergences in the published results (in particular, between those obtained by EPR and NMR). (iii) The apparent dissociation constants of Zn(Aβ) in various buffers are in the range of 1 to 20 μM (a 10 times lower conditional dissociation constant can be estimated. (iv) For the Zn(II) coordination, the implication of the three His and the Asp1 residues is consensual. The Asp1 can be coordinated by the carboxylate and/or the N-terminus functions. Additional ligands are possible, such as Glu11 or H₂O.