It was conjectured by John Milnor in 1968 that the fundamental group of a complete Riemannian manifold with nonnegative Ricci Curvature is finitely generated. I will present joint work with Elia Bruè and Aaron Naber where we construct a family of manifolds with nonnegative Ricci Curvature and infinitely generated fundamental group, thus providing a counterexample to the Milnor conjecture.