The accumulation of the amyloid-β peptides (Aβ) is central to the development of Alzheimer's disease. The mechanism by which Aβ triggers a cascade of events that leads to dementia is a topic of intense investigation. Aβ self-associates into a series of complex assemblies with different structural and biophysical properties. It is the interaction of these oligomeric, protofibril and fibrillar assemblies with lipid membranes, or with membrane receptors, that results in membrane permeability and loss of cellular homeostasis, a key event in Alzheimer's disease pathology. Aβ can have an array of impacts on lipid membranes, reports have included: a carpeting effect; a detergent effect; and Aβ ion-channel pore formation. Recent advances imaging these interactions are providing a clearer picture of Aβ induced membrane disruption. Understanding the relationship between different Aβ structures and membrane permeability will inform therapeutics targeting Aβ cytotoxicity.