The far-infrared excesses produced by debris disks are common features of stellar systems. These disks are thought to contain solids ranging from micron-sized dust to planetesimals. Naturally, their formation and evolution are linked to those of potential planets. With this motivation, the Herschel open time key programme DUNES (DUst around NEarby Stars) aims at further characterising known debris disks and discovering new ones in the regime explored by the Herschel space observatory. On the one hand, in their survey of 133 nearby FGK stars, DUNES discovered a class of extremely cold and faint debris disks, different from well-known disks such as the one around Vega in that their inferred typical grain sizes are rather large, indicating low dynamical excitation and low collision rates. On the other hand, for the more massive disk around the sun-like star HD 207129, well-resolved PACS images confirmed the ring-liked structure seen in HST images and provided valuable information for an in-depth study and benchmark for models. Employing both models for power-law fitting and collisional evolution we found the disk around HD 207129 to feature low collision rates and large grains, as well. Transport by means of Poynting-Robertson drag likely plays a role in replenishing the dust seen closer to the star, inside of the ring. The inner edge is therefore rather smooth and the contribution from the extended halo of barely bound grains is small. Both slowly self-stirring and planetary perturbations could potentially have formed and shaped this disk. Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.