The presence of fibrillar protein deposits (amyloid) of human islet amyloid polypeptide (hIAPP) in the pancreatic islets of Langerhans is thought to be related to death of the insulin-producing islet β-cells in type 2 diabetes mellitus (DM2). The mechanism of hIAPP-induced β-cell death is not understood. However, there is growing evidence that hIAPP-induced disruption of β-cell membranes is the cause of hIAPP cytotoxicity. Amyloid cytotoxicity by membrane damage has not only been suggested for hIAPP, but also for peptides and proteins related to other misfolding diseases, like Alzheimer’s disease, Parkinson’s disease, and prion diseases. Here we review the interaction of hIAPP with membranes, and discuss recent progress in the field, with a focus on hIAPP structure and on the proposed mechanisms of hIAPP-induced membrane damage in relation to β-cell death in DM2.