Abstract
The idea of an isolated system is a powerful abstraction to describe a system that is only weakly interacting with its environment and is mainly subject to intrinsic forces, in particular its own gravitational field. Mathematically, it is described as an asymptotically flat space-time. Such space-times can be geometrically characterized using their conformal structure, metrics which differ by a positive factor. The emphasis on conformal properties has many remarkable consequences: the existence of a boundary to space-time; the unique definition of gravitational radiation; the Bondi-Sachs mass-loss formula; asymptotic symmetries; global existence theorems. More recent developments include a remarkable appearance of equations of motion in the asymptotic regime and a “triangle” relationship with quantum field theoretical notions.