An evolving hypersurface of postive mean curvature that moves at each point in normal direction with speed given by the inverse of the mean curvature is called a solution of the inverse mean curvature flow. This flow is useful in General Relativity since it can be shown that certain integral quantities measuring energy are monotone under this flow. The lecture reviews joint work with Tom Ilmanen on the basic properties of the classical and weak formulation of the flow and describes recent new results on the optimal regularity and asymptotic behaviour of solutions.