The idea that alternative stable states may exist in communities has been a recurring theme in ecology since the late 1960s, and is now experiencing a resurgence of interest. Since the first papers on the subject appeared, two perspectives have developed to describe how communities shift from one stable state to another. One assumes a constant environment with shifts in variables such as population density, and the other anticipates changes to underlying parameters or environmental “drivers”. We review the theory behind alternative stable states and examine to what extent these perspectives are the same, and in what ways they differ. We discuss the concepts of resilience and hysteresis, and the role of stochasticity within the two formulations. In spite of differences in the two perspectives, the same type of experimental evidence is required to demonstrate the existence of alternative stable states.