  A lot of progress has been made recently in our understanding of the
random-field Ising model thanks to large-scale numerical simulations. In
particular, it has been shown that, contrary to previous statements: the
critical exponents for different probability distributions of the random fields
and for diluted antiferromagnets in a field are the same. Therefore, critical
universality, which is a perturbative renormalization-group prediction, holds
beyond the validity regime of perturbation theory. Most notably, dimensional
reduction is restored at five dimensions, i.e., the exponents of the
random-field Ising model at five dimensions and those of the pure Ising
ferromagnet at three dimensions are the same.
