Amyloid fibrils occur inside the human body, associated with ageing or a group of diseases that includes, amongst others, Alzheimer's disease, atherosclerosis and type II diabetes. Many natural polypeptide chains are able to form amyloid fibrils in vivo or in vitro, and this ability has been suggested to represent an inherent consequence of the chemical structure of the polypeptide chain. Recent literature has provided a wealth of information about the structure of aggregates, precipitates, amyloid fibrils and other types of fibrillar polypeptide assemblies. However, the biophysical meaning associated with these terms can differ considerably depending on the context of their usage. This overview presents a structural comparison of amyloid fibrils and other types of polypeptide assemblies and defines amyloid fibrils, based on structural considerations, as fibrillar polypeptide aggregates with a cross-beta conformation.