ag.algebraic geometry - Moduli space of flat bundles

Is there a good place to learn about the structure of moduli stack of flat $G$-bundles on an algebraic curve?

Of course, we're just studying representations of a group $pi_1(X)to G$ modulo some conjugation (that's why it should be a stack). Since this is very similar to Galois representations in number theory, I wonder if there's a reference that also explains the similarities and differences between the two cases.