The functional renormalization group is an ideal tool for dealing with the diversity of energy scales and competition of correlations in interacting Fermi systems. Starting point is an exact hierarchy of flow equations which yields the gradual evolution from a microscopic model Hamiltonian to the effective low-energy action as a function of a continuously decreasing energy cutoff. Suitable truncations of the hierarchy have recently led to powerful new approximation schemes. Applications to be discussed in the talk include: i) d-wave superconductivity and other instabilities in the two-dimensional Hubbard model, ii) transport through a barrier and resonant tunneling in a one-dimensional Luttinger liquid metal