We study ferromagnetic and antiferromagnetic Ising models in contact with a heat reservoir, and subject to an external source of energy. The contact with the heat bath is simulated by a single-spin flip Glauber dynamics, while the flux of energy is simulated by the two-spin exchange Kawasaki process. Pair approximation and Monte Carlo calculations are employed to determine the phase diagram for the stationary states of the model. We report the results we have obtained in one, two and three dimensions. For instance, in one dimension, while the pair approximation predicts a phase transition for the ferromagnetic case, this is not corroborated by the Monte Carlo simulations. We also use Monte Carlo simulations to evaluate the static and dynamic critical exponents at the transition lines between nonequilibrium steady states. We show that the critical exponents agree with those of the corresponding equilibrium Ising model, for which detailed balance is obeyed.