Our PACS and SPIRE images of the Aquila Rift and part of the Polaris Flare regions, taken during the science demonstration phase of Herschel discovered fascinating, omnipresent filamentary structures that appear to be physically related to compact cores. We briefly describe a new multi-scale, multi-wavelength source extraction method used to detect objects and measure their parameters in our Herschel images. All of the extracted starless cores (541 in Aquila and 302 in Polaris) appear to form in the long and very narrow filaments. With its combination of the far-IR resolution and sensitivity, Herschel directly reveals the filaments in which the dense cores are embedded; the filaments are resolved and have deconvolved widths of similar to 35 '' in Aquila and similar to 59 '' in Polaris (similar to 9000 AU in both regions). Our first results of observations with Herschel enable us to suggest that in general dense cores may originate in a process of fragmentation of complex networks of long, thin filaments, likely formed as a result of an interplay between gravity, interstellar turbulence, and magnetic fields. To unravel the roles of the processes, one has to obtain additional kinematic and polarization information; these follow-up observations are planned.