We present new developments in the dual hierarchical approach to singular mean-field limits. Combining this method with a refined analysis of dual BBGKY hierarchies based on kinetic regularity estimates, we establish the mean-field limit for interaction forces in L^{2-\eta}, for all sufficiently small \eta>0. In particular, this yields the first derivation of the 2D Vlasov-Poisson equation from classical particle dynamics with Coulomb interactions. A further development of the method also allows us to capture fluctuations around the mean-field limit and to justify the corresponding fluctuating Vlasov equation in the same singular regime. The results are global in time as long as the mean-field solution remains sufficiently regular. This is joint work with P.-E. Jabin.