Since Pietrowsky's first analytical study of collisional systems of asteroids (1953), through Dohnanyi's comprehensive theory (1969), to the analytical and numerical studies of the last two decades, the collisional evolution of populations of asteroids — and to a less extent, of Trojans and TNOs— has been investigated by many researchers.
The study of such systems is an intrinsically delicate mathematical problem, as their evolution in time is properly described in terms of systems of first–order, non–linear differential equations. Physically, the limited knowledge of some of the collisional properties, rotations and internal structure of bodies, and the complex interplay with dust, non–gravitational effects and dynamical interactions with planets, make the study of the collisional evolution a hard multi–parametric problem. Nevertheless, the task is worth the effort, in fact the understanding of evolutionary processes in the solar system's small body belts provides the main tools to discriminate between the many different theoretical scenarios proposed to explain the formation of the solar system itself.
This review tries to give an updated overall view of the research done in this field, and to show the connections between apparently independent phenomena that may affect the evolution of collisional systems of asteroids and TNOs.