Abstract: The virtual n-th betti number of a finitely generated group G is defined as the supremum over dim_Q(H_2(H;Q)), where H runs through all finite index subgroups of G. We will show that the only examples of finitely generated and residually free groups, with a finite virtual second betti number, are the obvious ones: free, surface and free abelian groups. We will also discuss how virtual (co)homology (with coefficients in a finite field) can serve as a profinite invariant, and use this to resolve a specific case of a conjecture of Bridson and Reid about the profinite rigidity of direct products of free and surface groups (joint work with Morales).