  We consider d-dimensional random surface models which for d=1 are the
standard (tied-down) random walks (considered as a random ``string''). In
higher dimensions, the one-dimensional (discrete) time parameter of the random
walk is replaced by the d-dimensional lattice \Z^d, or a finite subset of it.
The random surface is represented by real-valued random variables \phi_i, where
i is in \Z^d. A class of natural generalizations of the standard random walk
are gradient models whose laws are (formally) expressed as
  P(d\phi) = 1/Z \exp[-\sum_{|i-j|=1}V(\phi_i-\phi_j)] \prod_i d\phi_i,
  V:\R -> R^+ convex, and with some growth conditions. Such surfaces have been
  introduced in theoretical physics as (simplified) models for random
interfaces separating different phases. Of particular interest are
localization-delocalization phenomena, for instance for a surface interacting
with a wall by attracting or repulsive interactions, or both together. Another
example are so-called heteropolymers which have a noise-induced interaction.
Recently, there had been developments of new probabilistic tools for such
problems. Among them are: o Random walk representations of Helffer-Sj\"ostrand
type, o Multiscale analysis, o Connections with random trapping problems and
large deviations We give a survey of some of these developments.
