  We discuss the non-equilibrium critical phenomena in liquids, and the models
for these phenomena based on local equilibrium and extended scaling
assumptions. Special situations are proposed for experimental tests of the
theory. Near-critical steady and transient states are reviewed. In a
near-critical steady state characterized by a temperature gradient, the theory
predicts strong nonequilibrium fluctuations at very large length scales. Close
to the critical point, this results in a nonlinear regime of heat conductivity.
A transient non-equilibrium state triggered by a rapid and large spatially
uniform perturbation of the critical liquid is considered. A step away from
criticality generates a free field with strong and decaying correlations in
initial state, while a step towards criticality initiates the increase of
fluctuations and of their correlation at the large scale edge of the critical
range. The approach to equilibrium is characterized by an equilibration length
\Lambda_eq that depends on time t. The theory predicts a power law approach of
the temperature to the new equilibrium; the new critical exponents depend on
whether the temperature is initially increased or decreased.
