Collisions near threshold in atomic and molecular physics

We review topics of current interest in the physics of electronic, atomic a nd molecular scattering in the vicinity of thresholds. Starting from phase space arguments, we discuss the modifications of the Wigner law that are re quired to deal with scattering by Coulomb, dipolar and dispersion potential s, as well as aspects of threshold behaviour observed in ultracold atomic c ollisions. We employ the tools of quantum defect and semiclassical theories to bring out the rich variety of threshold behaviours. The discussion is t hen turned to recent progress in understanding threshold behaviour of many- body break-ups into both charged and neutral species, including both Wannie r double ionization and three-body recombination in ultracold gases. We emp hasize the dominant role that hyperspherical coordinate methods have played in understanding these problems. We assess the effects of external fields on scattering, and the corresponding modification of phase space that alter s the Wigner law. Threshold laws in low dimensions and examples of their ap plications to specific collision processes are discussed.