  The interstellar medium contains filamentary structure over a wide range of
scales. Understanding the role of this structure, both as a conduit of gas
across the scales and a diagnostic tool of local physics, is a major focus of
star formation studies. We review recent progress in studying filamentary
structure in the ISM, interpreting its properties in terms of physical
processes, and exploring formation and evolution scenarios. We include
structures from galactic-scale filaments to tenth-of-a-parsec scale filaments,
comprising both molecular and atomic structures, from both observational and
theoretical perspectives. In addition to the literature overview, we assemble a
large amount of catalogue data from different surveys and provide the most
comprehensive census of filamentary structures to date. Our census consists of
22 803 filamentary structures, facilitating a holistic perspective and new
insights. We use our census to conduct a meta-analysis, leading to a
description of filament properties over four orders of magnitudes in length and
eight in mass. Our analysis emphasises the hierarchical and dynamical nature of
filamentary structures. Filaments do not live in isolation, nor they generally
resemble static structures close to equilibrium. We propose that accretion
during filament formation and evolution sets some of the key scaling properties
of filaments. This highlights the role of accretion during filament formation
and evolution and also in setting the initial conditions for star formation.
Overall, the study of filamentary structures during the past decade has been
observationally driven. While great progress has been made on measuring the
basic properties of filaments, our understanding of their formation and
evolution is clearly lacking. In this context, we identify a number of
directions and questions we consider most pressing for the field.
