The moduli space of stable rank r vector bundles on curves is diffeomorphic to the U(r)-character variety via famous theorem of Narasimhan-Seshadri. Similarly, the moduli space of stable rank r Higgs bundles  on curves is diffeomorphic to the GL(r)-character variety via non-abelian Hodge correspondence. In this talk, I will give a brief introduction to these moduli spaces, character varieties and some cohomological implications of these diffeomorphisms.