Bioinspired fibrous materials that span the nano-to-meso scales have potentially broad applications in nanobiotechnology; for instance, as scaffolds in 3D cell culture and tissue engineering, and as templates for the assembly of other polymer and inorganic materials. The field is burgeoning, and this review is necessarily focused. It centres on recent developments in the design of peptide-based fibres and particularly those using the alpha-helix and the collagen triple helix as building blocks for self-assembly. Advances include new designs in both categories, the assembly of more-complex topologies using fibres themselves as building blocks, and the decoration of the assembled materials with functional moieties.