  Many non-equilibrium systems display dynamic phase transitions from active to
absorbing states, where fluctuations cease entirely. Based on a field theory
representation of the master equation, the critical behavior can be analyzed by
means of the renormalization group. The resulting universality classes for
single-species systems are reviewed here. Generically, the critical exponents
are those of directed percolation (Reggeon field theory), with critical
dimension d_c = 4. Yet local particle number parity conservation in
even-offspring branching and annihilating random walks implies an inactive
phase (emerging below d_c' = 4/3) that is characterized by the power laws of
the pair annihilation reaction, and leads to different critical exponents at
the transition. For local processes without memory, the pair contact process
with diffusion represents the only other non-trivial universality class. The
consistent treatment of restricted site occupations and quenched random
reaction rates are important open issues.
