Comets, comet-like objects and their fragments are the most plausible source for the dust in both the inner heliosphere and planetary debris discs around other stars. The smallest size of dust particles in debris discs is not known and recent observational results suggest that the size distribution of the dust extends down to sizes of a few nanometres or a few tens of nanometres. In the Solar System, electric field measurements from spacecraft observe events that are explained with high-velocity impacts of nanometre-sized dust. In some planetary debris discs an observed mid- to near-infrared emission supposedly results from hot dust located in the vicinity of the star. And the observed emission is characteristic of dust of sizes a few tens ...