  We review the main tools which allow for the statistical characterization of
weighted networks. We then present two case studies, the airline connection
network and the scientific collaboration network, which are representative of
critical infrastructures and social systems, respectively. The main empirical
results are (i) the broad distributions of various quantities and (ii) the
existence of weight-topology correlations. These measurements show that weights
are relevant and that in general the modeling of complex networks must go
beyond topology. We review a model which provides an explanation for the
features observed in several real-world networks. This model of weighted
network formation relies on the dynamical coupling between topology and
weights, considering the rearrangement of weights when new links are introduced
in the system.
