  In this paper we first give a brief overview of Monte Carlo simulation
results obtained by applying the Damage Spreading method. We analyse the
transition between a state where the damage becomes healed (the frozen phase)
and a regime where the damage spreads arriving at a finite (stationary) value
(the damaged phase), when a control parameter is finely tuned. These kinds of
transitions are actually true irreversible phase transitions themselves, and
the issue of their universality class is also discussed.
  Subsequently, the attention is focused on the propagation of damage in
magnetic systems placed in confined geometries, such as the Abraham's Model,
the standard Ising magnet (Glauber dynamics) and the corner geometry. The
influence of interfaces between magnetic domains of different orientation on
the spreading of the perturbation is also discussed, showing that the presence
of interfaces enhances the propagation of the damage. Furthermore, the critical
transition between propagation and nonpropagation of the damage is discussed.
In all cases, the determined critical exponents suggest that the DS transition
does not belong to the universality class of Directed Percolation, unlike many
other systems exhibiting irreversible phase transitions. This result reflects
the dramatic influence of interfaces on the propagation of perturbations in
magnetic systems.
