Proteinaceous materials based on the amyloid core structure have recently been discovered at the origin of biological functionality in a remarkably diverse set of roles, and attention is increasingly turning towards such structures as the basis of artificial self‐assembling materials. These roles contrast markedly with the original picture of amyloid fibrils as inherently pathological structures. Here we outline the salient features of this class of functional materials, both in the context of the functional roles that have been revealed for amyloid fibrils in nature, as well as in relation to their potential as artificial materials. We discuss how amyloid materials exemplify the emergence of function from protein self‐assembly at multiple length scales. We focus on the connections between mesoscale structure and material function, and demonstrate how the natural examples of functional amyloids illuminate the potential applications for future artificial protein based materials. Amyloid materials have recently been discovered at the origin of biological functionality and attention is increasingly turning toward their use in artificial materials. These roles contrast markedly with their original picture as pathological materials. A unified view of this class of functional materials, both in their natural roles and as synthetic materials, is given, and how function emerges directly from the hierarchical protein self‐assembly process is illustrated.