Isolated gravitating systems are modelled by Lorentzian 4-manifolds resembling Minkowski space at large distances. It is an important task of Mathematical Relativity to use structures from differential geometry to model calssical physical concepts such as mass, center of mass, local or global energy and momentum. The lecture explains how foliations by hypersurfaces of prescribed curvature can be used in a geometrically natural way to construct the desired structures having the correct physical properties.