  We give an overview of the state of the art of the analysis of disordered
models of pinning on a defect line. This class of models includes a number of
well known and much studied systems (like polymer pinning on a defect line,
wetting of interfaces on a disordered substrate and the Poland-Scheraga model
of DNA denaturation). A remarkable aspect is that, in absence of disorder, all
the models in this class are exactly solvable and they display a
localization-delocalization transition that one understands in full detail.
Moreover the behavior of such systems near criticality is controlled by a
parameter and one observes, by tuning the parameter, the full spectrum of
critical behaviors, ranging from first order to infinite order transitions.
This is therefore an ideal set-up in which to address the question of the
effect of disorder on the phase transition,notably on critical properties. We
will review recent results that show that the physical prediction that goes
under the name of Harris criterion is indeed fully correct for pinning models.
Beyond summarizing the results, we will sketch most of the arguments of proof.
