  This review addresses recent developments in nonequilibrium statistical
physics. Focusing on phase transitions from fluctuating phases into absorbing
states, the universality class of directed percolation is investigated in
detail. The survey gives a general introduction to various lattice models of
directed percolation and studies their scaling properties, field-theoretic
aspects, numerical techniques, as well as possible experimental realizations.
In addition, several examples of absorbing-state transitions which do not
belong to the directed percolation universality class will be discussed. As a
closely related technique, we investigate the concept of damage spreading. It
is shown that this technique is ambiguous to some extent, making it impossible
to define chaotic and regular phases in stochastic nonequilibrium systems.
Finally, we discuss various classes of depinning transitions in models for
interface growth which are related to phase transitions into absorbing states.
