Though nonequilibrium phenomena abound in nature, they are still only very poorly understood at a fundamental level. Even the study of nonequilibrium steady states, as the simplest generalizations of thermal equilibrium, is still in its early stages. However, investigations of simple model systems have revealed a wealth of unexpected behavior which can appear highly counterintuitive when compared to our equilibrium-trained expectations.

In my talk, I will briefly review equilibrium statistical mechanics and then discuss, and demonstrate "live," a simple nonequilibrium model, whose physical applications include traffic, microemulsions and electrophoresis. In equilibrium, its properties are completely trivial. Once driven into a nonequilibrium steady state, however, it develops a line of phase transitions, reminiscent of traffic jams. Different ordered phases, including a topologically interesting one, appear to coexist, and we do not know how each is selected. The growth of ordered domains also still remains a largely unsolved problem. I will conclude with an outlook and a list of open questions.