Form and function in biological filaments: a physicist's review

Nature uses elongated shapes and filaments to build stable structures, generate motion and allow complex geometric interactions. In this review, we examine the role of biological filaments across different length scales. From the molecular scale, where cytoskeletal filaments provide a robust but dynamic cellular scaffolding, over the scale of cellular appendages like cilia and flagella, to the scale of filamentous microorganisms like cyanobacteria, among the most successful genera on Earth, and even to the scale of elongated animals like worms and snakes, whose motility modes inspire robotic analogues. We highlight the general mechanisms that couple form and function. We discuss physical principles and models, such as classical elasticity and the non-reciprocity of active matter, that can be used to trace unifying themes linking these systems across approximately nine orders of magnitude in length.This article is part of the theme issue 'Biological fluid dynamics: emerging directions'.