Aberrant aggregation of the Aβ protein is a hallmark of Alzheimer’s disease (AD), but no complete characterization of the molecular level pathogenesis has been achieved. A promising hypothesis is that dysfunction of metal ion homeostasis, and consequently, the undesired interaction of metal ions with Aβ, may be central to the development of AD. Qualitatively, most data indicate that Cu(II) induces rapid self-assembly of both Aβ40 and Aβ42 during the initial phase of the aggregation, while at longer time scales fibrillation may occur, depending on the experimental conditions. For Aβ40 and Cu(II):Aβ ≤ 1, most data imply that low concentration of Aβ40 favors nucleation and rapid fibril elongation, while high concentration of Aβ40 favors formation of amorphous aggregates. However, there are conflicting reports on this issue. For Aβ42 and Cu(II):Aβ ≤ 1, there is consensus that the lag time is extended upon addition of Cu(II). For Cu(II):Aβ > 1, the lag time is increased upon interaction with Cu(II), and in most cases fibrillation is not observed, presumably because Cu(II) occupies a second more solvent-exposed binding site, which is more prone to form metal ion-bridged species and cause rapid formation of non-fibrillar aggregates. The interesting N-terminally truncated Aβ11–40 with high affinity for Cu(II), exhibits delay of fibrillation upon addition of 0.4 eq. Cu(II). In our view, there are still problems achieving reproducible results in this field, and we provide a shortlist of some of the pitfalls. Finally, we propose a consensus model for the effects of Cu(II) on the aggregation kinetics of Aβ.