Identification by the Ulysses spacecraft of interstellar grains inside the planetary system provides a new window for the study of diffuse interstellar matter. Dust particles observed by Ulysses and confirmed by Galileo are more massive (≥10-13 g) than the classical interstellar grains. Even bigger grains (≈10-7 g) were observed in form of interstellar meteors. We analyze the consequences of the plentiful existence of massive grains in the diffuse interstellar medium. Astronomically observed classical interstellar grains can be described by a size distribution ranging from ~5 to 250 nm in radius (~10-18 to 10-13 g). Lifetimes of these particles, owing to mutual collisions in interstellar space, can be as short as 105f years, where f=10 to 1000, is the fraction of total lifetime to the time when grains are exposed to supernova shocks. Shattering is a source of the smallest of these grains, but grains more massive than ~10-16 g of the classical interstellar grain population are rapidly destroyed. When applying the same shattering mechanism to the more massive grains found recently, we suggest that collisions of particles bigger than ~10-15 g provide a source for smaller grains. Because massive grains couple to the interstellar gas only over large (100 to 1000 pc) length scales, the cosmic abundance ratio of gas-to-dust needs only to be preserved averaged over corresponding volumes of space. ¿ 2000 American Geophysical Union