The first part of the chapter is a not-so-small presentation of equilibrium phase transitions, which allows us to introduce key concepts for both equilibrium and nonequilibrium phase transitions. The lattice gas, that is, the Ising model with a conserved order parameter, is an appropriate model to analyze how an equilibrium model can be brought out of equilibrium and to highlight the importance of boundary conditions in nonequilibrium phase transitions. The driven lattice gas, introduced by Katz, Lebowitz, and Spohn around 40 years ago, allows to define the totally asymmetric simple exclusion (TASEP) model and subsequently also the BRIDGE model. The latter is a one-dimensional model displaying a nonequilibrium phase transition with a symmetry breaking between two equivalent classes of particles. This result, considering the short-range character of interactions, would not be possible at equilibrium. In an equally unexpected way, an external breaking of the symmetry (equivalent to the application of a magnetic field to the Ising model) does not make the phase transition disappear.