In the past few years, revolutionary advances in experimental techniques and spectacular increases in computer power have offered unique opportunities to develop a much more profound understanding of the atomic few-body problem. One area of intense effort is the study of fragmentation processes – break-up processes – which are studied experimentally by detecting in coincidence the collisional fragments with their angles and energies resolved. These experiments offer a unique insight into the delicacies of atomic and molecular interactions, being at the limit of what is quantum mechanically knowable; the fine detail that is revealed would be swamped in a less differential measurement. The challenge for the theorist is to develop mathematical and computational techniques which are of sufficient ingenuity and sophistication that they can elucidate the Physics observed in existing measurements and give direction to the next generation of experiments. Fragmentation processes are studied by those interested in electron and photon impact ionization, heavy particle collisions, collisions involving antimatter, as well as molecular collisions.