  We have developed a nonperturbative functional renormalization group approach
for random field models and related disordered systems for which, due to the
existence of many metastable states, conventional perturbation theory often
fails. The approach combines an exact renormalization group equation for the
effective average action with a nonperturbative approximation scheme based on a
description of the probability distribution of the renormalized disorder
through its cumulants. For the random field $O(N)$ model, the minimal
truncation within this scheme is shown to reproduce the known perturbative
results in the appropriate limits, near the upper and lower critical dimensions
and at large number $N$ of components, while providing a unified
nonperturbative description of the full $(N,d)$ plane, where $d$ is the spatial
dimension.
