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Understanding how stars form in the cold interstellar medium of galaxies is a fundamental issue in modern astrophysics. Large scale Herschel and Planck observations of submillimeter dust emission revealed the omnipresence of filamentary structures in the interstellar medium (ISM). The ubiquity of filaments in quiescent clouds as well as in star-forming regions indicates that the formation of filamentary structures takes place before any star formation activity and that it is a natural product of the physics at play in the magnetized turbulent ISM. Moreover, the spatial distribution of star forming cores observed mainly along the densest filaments suggests that the properties of interstellar filaments are a key element defining the initial conditions required for the onset of star formation. Hence, describing filament properties by detailed observations tracing gas and dust in total and polarized intensities, and understanding the results of realistic numerical simulations as well as analytical calculations, are essential to make progress in our understanding of the physical processes involved in the formation and evolution of interstellar filaments and their role in the star formation process.