  Scaling ideas and renormalization group approaches proved crucial for a deep
understanding and classification of critical phenomena in thermal equilibrium.
Over the past decades, these powerful conceptual and mathematical tools were
extended to continuous phase transitions separating distinct non-equilibrium
stationary states in driven classical and quantum systems. In concordance with
detailed numerical simulations and laboratory experiments, several prominent
dynamical universality classes have emerged that govern large-scale, long-time
scaling properties both near and far from thermal equilibrium. These pertain to
genuine specific critical points as well as entire parameter space regions for
steady states that display generic scale invariance. The exploration of
non-stationary relaxation properties and associated physical aging scaling
constitutes a complementary potent means to characterize cooperative dynamics
in complex out-of-equilibrium systems. This article describes dynamic scaling
features through paradigmatic examples that include near-equilibrium critical
dynamics, driven lattice gases and growing interfaces, correlation-dominated
reaction-diffusion systems, and basic epidemic models.
