At the edge of the Solar System lies the Kuiper Belt, a ring of leftover planetesimals from the era of planet formation. Collisions between the Kuiper Belt Objects produce dust grains, which absorb and re-radiate stellar radiation. The total amount of stellar radiation so absorbed is perhaps one part in ten million. Analogous to this, Sun-like stars at Sun-like ages commonly have dusty debris disks, which absorb and re-radiate as much as one part in ten thousand of the stellar radiation. We set out to understand this difference. In chapter 1, we outline the relevant observations and give a feel for the relevant physics. In chapter 2, we turn to the extrasolar debris disks. Using disks spanning a wide range of ages, we construct a pseudo-evolution sequence for extrasolar debris disks. We apply a straightforward collision model to this sequence, and find that the brightest disks are a hundred to a thousand times as massive as the Kuiper Belt, which causes the difference in dust luminosity. Current theoretical models of planetesimal growth predict very low efficiency in making large planetesimals, such that the Kuiper Belt should be the typical outcome of Minimum Mass Solar Nebula type disks. These models cannot produce the massive disks we find around other stars. We revisit these models in chapter 3, to understand the origin of this low efficiency. We confirm that these models, which begin with kilometer sized planetesimals, cannot produce the observed extrasolar debris disks. Instead, we propose an alternate model where most mass begins in centimeter sized grains, with some kilometer sized seed planetesimals. In this model, collisional cooling amongst the centimeter grains produces a new growth mode. We show in chapter 4 that this can produce the Kuiper Belt from a belt not much more massive than the Kuiper Belt today. We follow in chapter 5 by showing that this model can also produce the massive planetesimal populations needed to produce extrasolar debris disks.