  We present a non-perturbative renormalization-group approach to the
Bose-Hubbard model. By taking as initial condition of the RG flow the (local)
limit of decoupled sites, we take into account both local and long-distance
fluctuations in a nontrivial way. This approach yields a phase diagram in very
good quantitative agreement with the quantum Monte Carlo results and reproduces
the two universality classes of the superfluid--Mott-insulator transition with
a good estimate of the critical exponents. Furthermore, it reveals the crucial
role of the "Ginzburg length" as a crossover length between a weakly- and a
strongly-correlated superfluid phase.
