This paper reviews simulational and theoretical investigations of critical behavior in a stochastic, interacting lattice gas under the influence of a uniform external driving field. By studying this model system one wishes to gain a deeper understanding of steady states far from thermal equilibrium, and their dynamic universality classes. The major result in the case of attractive particle-particle interactions is the emergence of a novel non-equilibrium fixed point, different from the Wilson-Fisher fixed point of the equilibrium system. The fluctuations of internal energy, the structure factor and the two-point correlations all display surprising features associated with the non-equilibrium nature of the system. For repulsive interactions and small driving forces, one finds a continuous, Ising-like transition which turns first order for larger fields until it is completely destroyed.
Influence of initial states and structure defects on non-equilibrium critical behavior of 3D and 2D Ising models