Alzheimer’s disease is the most common form of dementia and its pathological hallmarks include the loss of neurones through cell death, as well as the accumulation of amyloid fibres in the form of extracellular neuritic plaques. Amyloid fibrils are composed of the amyloid-β peptide (Aβ), which is known to assemble to form ‘toxic’ oligomers that may be central to disease pathology. Aβ is produced by cleavage from the amyloid precursor protein within the transmembrane region, and the cleaved peptide may retain some membrane affinity. It has been shown that Aβ is capable of specifically binding to phospholipid membranes with a relatively high affinity, and that modulation of the composition of the membrane can alter both membrane–amyloid interactions and toxicity. Various biomimetic membrane models have been used (e.g. lipid vesicles in solution and tethered lipid bilayers) to examine the binding and interactions between Aβ and the membrane surfaces, as well as the resulting permeation. Oligomeric Aβ has been observed to bind more avidly to membranes and cause greater permeation than fibrillar Aβ. We review some of the recent advances in studying Aβ–membrane interactions and discuss their implications with respect to understanding the causes of Alzheimer’s disease.