Aβs are peptide fragments of 39 to 43 amino acid length, most often found as Aβ1-40 or Aβ1-42, that result from the proteolytic cleavage of the transmembrane amyloid precursor protein. Directly after cleavage, the membrane-associated Aβs dissociate from the membrane as monomers with nonstructured and α-helical regions. The following complex sequence of events involving extensive structural transitions of Aβ is macroscopically summarized as the nucleation-growth mechanism: after nucleation seeds have formed during an initial lag-phase, aggregation first follows an exponential growth phase, and finally reaches a plateau during the saturation phase. Along this process, Aβ is suggested to form various β-sheet structures until it (mis)folds into mature parallel β-sheet fibril plaques. The lipid membrane is proposed to act as a catalyst in the disorder-to-order transitions and, thus, the misfolding of the peptide. In particular, lipid charge and membrane composition can alter the misfolding trajectory, with negatively charged lipids having been observed to support the aggregation considerably. As such, it has been suggested that already during the lag-phase, that is when no macroscopic misfolded Aβ fibrils have been formed yet, Aβ already accumulates as small oligomeric intermediates that can lead to membrane damage and toxicity in neurodegenerative diseases. Various models for such toxicity have been proposed that are reminiscent of the mechanism of antimicrobial peptides, where either Aβ-transmembrane incorporation is necessary to form pores or interfacial Aβ-membrane interactions destabilize the membrane via a carpet model-like mechanism. According to these models various potential α-helical or βsheet-based structures have resulted from computational approaches, many of which have yet to be verified.