Character varieties for a Riemann surface X are affine varieties parametrising representations of the fundamental group of X and so the local systems on the variety. The study of the geometry of character varieties and the computation of their cohomology is extremely interesting, especially because of their connection with the moduli spaces of Higgs bundles via non abelian Hodge correspondence. In this talk, I will explain how this setting translates for non-orientable real surfaces and how this is related to some interesting involutions on the moduli space of Higgs bundles. The cohomology of character varieties for non-orientable surfaces is way less known and I will explain also some of the recent advances in this subject