  The explicit calculation of the scaling form of the two-time autocorrelation
function in phase-ordering kinetics and in those cases of non-equilibrium
critical dynamics where the dynamical exponent z=2 through the extension of
dynamical scaling to local scale-invariance is reviewed. Conceptually, this
mainly requires an extension from the usually considered d-dimensional ageing
or Schr\"odinger algebras to a new kind of representation of the conformal
algebra in d+2 dimensions. Explicit tests in several exactly solved models of
simple magnets and through simulations in the 2D Ising and q-states Potts
models (q=2,3,8) quenched to T<T_c are presented and the extension to systems
with non-equilibrium steady-states is discussed through two exactly solvable
models as well. In the context of surface growth models, possible
generalizations for a dynamical exponent z=4 and beyond are discussed.
