Summary: The Dehn function of a finitely presented group measures in some sense the complexity of the word problem. It has a topological interpretation: given a homotopically trivial edge loop in a finite two-complex what is the minimal number of two-cells crossed during a homotopy to a point ? And a geometric interpretation: given a loop in the universal cover of a closed Riemannian manifold what is the area of a minimal filling surface ? There are only few arithmetic groups for which good estimates of the Dehn functions are known.