Abstract: In a seminal paper in 1983, Atiyah and Bott calculated the Betti numbers of the moduli space of holomorphic bundles over a complex curve using Morse theory of the Yang-Mills functional. In this talk, I will explain how to adapt the Atiyah-Bott method to calculate Z/2-Betti numbers of the moduli space of real/quaternionic vector bundles over a real curve. I will also report on work in progress on calculating rational Betti numbers.