Abstract The fibrillization of peptides is relevant to many diseases based on the deposition of amyloids. The formation of fibrils is being intensively studied, especially in terms of nanotechnology applications, where fibrillar peptide hydrogels are used for cell scaffolds, as supports for functional and responsive biomaterials, biosensors, and nanowires. This Review is concerned with fundamental aspects of the self‐assembly of peptides into fibrils, and discusses both natural amyloid‐forming peptides and synthetic materials, including peptide fragments, copolymers, and amphiphiles.