Modeling results show that collisions among Edgeworth-Kuiper Belt Objects (EKOs), a vast swarm of small bodies orbiting beyond Neptune, have been a major process affecting this population and its progeny, the short-period comets. Most EKOs larger than about 100 kilometers in diameter survive over the age of the solar system, but at smaller sizes collisional breakup is frequent, producing a cascade of fragments having a power law size-frequency distribution. Collisions are also a plausible mechanism for injecting EKOs 1 to 10 kilometers in diameter into dynamical resonances, where they can be transported into the inner solar system to become short-period comets. The fragmental nature of these comets may explain their physical properties, such as shape, color, and strength.