  Dynamical scaling arises naturally in various many-body systems far from
equilibrium. After a short historical overview, the elements of possible
extensions of dynamical scaling to a local scale-invariance will be introduced.
Schr\"odinger-invariance, the most simple example of local scale-invariance,
will be introduced as a dynamical symmetry in the Edwards-Wilkinson
universality class of interface growth. The Lie algebra construction, its
representations and the Bargman superselection rules will be combined with
non-equilibrium Janssen-de Dominicis field-theory to produce explicit
predictions for responses and correlators, which can be compared to the results
of explicit model studies.
  At the next level, the study of non-stationary states requires to go over,
from Schr\"odinger-invariance, to ageing-invariance. The ageing algebra admits
new representations, which acts as dynamical symmetries on more general
equations, and imply that each non-equilibrium scaling operator is
characterised by two distinct, independent scaling dimensions. Tests of
ageing-invariance are described, in the Glauber-Ising and spherical models of a
phase-ordering ferromagnet and the Arcetri model of interface growth.
