The functional renormalization group is an ideal tool for dealing with
the diversity of energy scales and competition of correlations in
interacting electron systems. An exact hierarchy of flow equations
yields the gradual evolution from a microscopic model Hamiltonian to
the effective action as a function of a continuously decreasing energy
cutoff. Suitable truncations of the hierarchy have recently led to
powerful new approximation schemes. I review applications of
truncated flow equations to the two-dimensional Hubbard model,
focussing in particular on magnetic correlations and d-wave
superconductivity, and to one-dimensional Luttinger liquids with
impurities, where a strikingly simple truncation captures a surprising
amount of non-trivial correlation effects.