Some changes are gradual and piecemeal but big structural shifts (phase transitions) have been a focus of complexity science work within many domains. Such transitions show many similarities, and they often show "emergent phenomena," properties not determined by any conditioning factors and a major focus of work in complexity science. But phase transitions are explained in quite different ways. This symposium will consider phase transitions in language acquisition as children develop explosively into competent users of a natural language system in the third year of life; the punctuated equilibrium model of changes in languages over time; dramatic tipping points in the way that infectious diseases spread; changes in species studied by evolutionary biologists; and the phase transitions studied by physicists that inspired broader-complexity science approaches. The focus will be on the commonalities and the differences in the way in which phase transitions are explained in different domains. Presentations will include formal, mathematical modeling and will address questions of what those models look like as phase transitions are taking place, before, during, and after.