In the first part of the talk, I will give an introduction to equivariant intersection theory as developed by Totaro, Edidin and Graham. I will then explain how equivariant techniques can be used in order to study the integral Chow ring of moduli of curves.

In the second part of the talk, I will focus on the computation, in terms of generators and relations, of the integral Chow ring of moduli of hyperelliptic curves of odd genus. Time permitting, I will discuss applications to other moduli spaces of curves.