Albert Fathi proved in the late 70's that the group of volume preserving homeomorphisms of the n-sphere is simple for n at least 3, but the case of the 2-sphere remained open until recently. In this talk, I will present results obtained in several works with Dan Cristofaro-Gardiner, Cheuk-Yu Mak, Sobhan Seyfaddini and Ivan Smith on the structure of the group of area preserving homeomorphisms of surfaces, which include in particular a solution of this problem. Even if the considered objects are not smooth (they are just homeomorphisms), the tools we use come from symplectic topology.