The Herschel Space Observatory provides a unique opportunity to improve our global understanding of the earliest phases of star formation. I will present an overview of the first results from the Gould Belt survey, one of the largest key projects with Herschel. The immediate objective of this imaging survey of nearby clouds is to obtain complete samples of prestellar cores and Class 0 protostars with well characterized luminosities, temperatures, and density profiles, as well as robust core mass functions in a variety of environments. The main scientific goal is to elucidate the physical mechanisms responsible for the formation of prestellar cores out of the diffuse interstellar medium. Our early findings confirm the existence of a close relationship between the prestellar core mass function (CMF) and the stellar initial mass function (IMF). The Herschel images also reveal a rich network of filaments in every interstellar cloud and suggest an intimate connection between the filamentary structure of the ISM and the formation process of prestellar cores. Remarkably, filaments are omnipresent even in unbound, non-star-forming complexes and seem to be characterized by a narrow distribution of widths around ˜ 0.1 pc. This characteristic width approximately corresponds to the sonic scale below which interstellar turbulence becomes subsonic in diffuse gas, supporting the view that the filaments may form as a result of the dissipation of large-scale turbulence. In active star-forming regions, most of the prestellar cores identified with Herschel are located within gravitationally unstable filaments above a critical threshold ˜ 15 M_⊙/pc in mass per unit length or ˜ 150 M_⊙/pc^2 in gas surface density. Altogether, the Herschel results favor a scenario in which interstellar filaments and prestellar cores represent two fundamental steps in the star formation process: First, large-scale magneto-hydrodynamic turbulence generates a complex web of filaments in the ISM; second, the densest filaments fragment and develop prestellar cores (and ultimately protostars) via gravitational instability.