  These notes are devoted to the statistical mechanics of directed polymers
interacting with one-dimensional spatial defects. We are interested in
particular in the situation where frozen disorder is present. These polymer
models undergo a localization/delocalization transition. There is a large
(bio)-physics literature on the subject since these systems describe, for
instance, the statistics of thermally created loops in DNA double strands and
the interaction between (1+1)-dimensional interfaces and disordered walls. In
these cases the transition corresponds, respectively, to the DNA denaturation
transition and to the wetting transition. More abstractly, one may see these
models as random and inhomogeneous perturbations of renewal processes.
  The last few years have witnessed a great progress in the mathematical
understanding of the equilibrium properties of these systems. In particular,
many rigorous results about the location of the critical point, about critical
exponents and path properties of the polymer in the two thermodynamic phases
(localized and delocalized) are now available.
  Here, we will focus on some aspects of this topic - in particular, on the
non-perturbative effects of disorder. The mathematical tools employed range
from renewal theory to large deviations and, interestingly, show tight
connections with techniques developed recently in the mathematical study of
mean field spin glasses.
