The hormone islet amyloid polypeptide (IAPP, or amylin) plays a role in glucose homeostasis but aggregates to form islet amyloid in type-2 diabetes. Islet amyloid formation contributes to β-cell dysfunction and death in the disease and to the failure of islet transplants. Recent work suggests a role for IAPP aggregation in cardiovascular complications of type-2 diabetes and hints at a possible role in type-1 diabetes. The mechanisms of IAPP amyloid formation in vivo or in vitro are not understood and the mechanisms of IAPP induced β-cell death are not fully defined. Activation of the inflammasome, defects in autophagy, ER stress, generation of reactive oxygen species, membrane disruption, and receptor mediated mechanisms have all been proposed to play a role. Open questions in the field include the relative importance of the various mechanisms of β-cell death, the relevance of reductionist biophysical studies to the situation in vivo, the molecular mechanism of amyloid formation in vitro and in vivo, the factors which trigger amyloid formation in type-2 diabetes, the potential role of IAPP in type-1 diabetes, the development of clinically relevant inhibitors of islet amyloidosis toxicity, and the design of soluble, bioactive variants of IAPP for use as adjuncts to insulin therapy.