Large scale geometry describes the properties of a metric space, which are invariant under quasi-isometries. The filling functions are such invariants. Roughly speaking, they measure how difficult it can get to fill a given boundary. I will introduce these functions for Riemannian manifolds and give an outline of their behaviour for spaces with curvature bounds. Further I will discuss some new results for filling functions for a class of nice-behaving nilpotent Lie groups.