P. Andre (CEA Saclay, Laboratoire AIM - Service d'Astrophysique, Gif-sur-Yvette, France),
J. Di Francesco (National Research Council Canada, Herzberg Institute of Astrophysics, Canada),
S.-I. Inutsuka (Nagoya University, Japan),
R. Pudritz (McMaster University, Origins Institute, Canada),
D. Ward-Thompson (University of Central Lancashire, Jeremiah Horrocks Institute, UK),
J. Pineda (University of Manchester, Jodrell Bank Centre for Astrophysics, United Kingdom)

We review recent progress in our understanding of the physics controlling the earliest evolutionary phases of star formation. Since PPV seven years ago, one area that has seen the most dramatic advances has been the characterization of the link between star formation and the structure of the cold interstellar medium (ISM). In particular, extensive studies of the nearest star-forming clouds of our Galaxy with the Herschel Space Observatory have provided us with unprecedented images of the initial and boundary conditions of the star formation process. The Herschel images reveal an intricate network of filamentary structures in every interstellar cloud. The observed filaments share common properties such as their central widths - but only the densest ones contain prestellar cores, the seeds of future stars. Overall, the Herschel submillimeter data, as well as other observations from, e.g., near- IR extinction studies, favor a scenario in which interstellar filaments and prestellar cores represent two key steps in the star formation process: first supersonic turbulence stirs up the gas, giving rise to a universal web-like structure in the ISM, then gravity takes over and controls the further fragmentation of filaments into prestellar cores and ultimately protostars. The new observational results connect remarkably well with nearly a decades worth of numerical simulations and theory which have consistently shown that the ISM should be highly filamentary on all scales and that star formation is intimately connected with self-gravitating filaments. We thus attempt to synthesize a comprehensive physical picture that arises from the confrontation of recent observations and simulations. We also emphasize how the apparent complexity of cloud structure and star formation may be governed by relatively simple universal processes - from filamentary clumps to galactic scales.

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