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The interstellar medium contains filamentary structure over a wide range ofscales. Understanding the role of this structure, both as a conduit of gasacross the scales and a diagnostic tool of local physics, is a major focus ofstar formation studies. We review recent progress in studying filamentarystructure in the ISM, interpreting its properties in terms of physicalprocesses, and exploring formation and evolution scenarios. We includestructures from galactic-scale filaments to tenth-of-a-parsec scale filaments,comprising both molecular and atomic structures, from both observational andtheoretical perspectives. In addition to the literature overview, we assemble alarge amount of catalogue data from different surveys and provide the mostcomprehensive census of filamentary structures to date. Our census consists of22 803 filamentary structures, facilitating a holistic perspective and newinsights. We use our census to conduct a meta-analysis, leading to adescription of filament properties over four orders of magnitudes in length andeight in mass. Our analysis emphasises the hierarchical and dynamical nature offilamentary structures. Filaments do not live in isolation, nor they generallyresemble static structures close to equilibrium. We propose that accretionduring filament formation and evolution sets some of the key scaling propertiesof filaments. This highlights the role of accretion during filament formationand evolution and also in setting the initial conditions for star formation.Overall, the study of filamentary structures during the past decade has beenobservationally driven. While great progress has been made on measuring thebasic properties of filaments, our understanding of their formation andevolution is clearly lacking. In this context, we identify a number ofdirections and questions we consider most pressing for the field.

Initial Conditions for Star Formation: A Physical Description of the Filamentary ISM