  A host of spatially extended systems, both in physics and in other
disciplines, are well described at a coarse-grained scale by a Langevin
equation with multiplicative-noise. Such systems may exhibit non-equilibrium
phase transitions, which can be classified into universality classes. Here we
study in detail one of such classes that can be mapped into a
Kardar-Parisi-Zhang (KPZ) interface equation with a positive (negative)
non-linearity in the presence of a bounding lower (upper) wall. The wall limits
the possible values taken by the height variable, introducing a lower (upper)
cut-off, and induce a phase transition between a pinned (active) and a depinned
(absorbing) phase. This transition is studied here using mean field and field
theoretical arguments, as well as from a numerical point of view. Its main
properties and critical features, as well as some challenging theoretical
difficulties, are reported. The differences with other multiplicative noise and
bounded-KPZ universality classes are stressed, and the effects caused by the
introduction of ``attractive'' walls, relevant in some physical contexts, are
also analyzed.
