The description of a general underlying structure for conversation has been the object of many studies. A good number of them have addressed the structure of turns, or a particular stage in a conversation---openings and closings, mainly---and only a few have attempted to cover the development of a dialogue from beginning to end. The latter have concentrated on very particular subgenres of conversation: task-oriented dialogues and the like. I will present a brief review of the achievements of those projects, and I will address the question of whether it is reasonable to expect to cover any dialogue and any dialogue type with a generalized structural description.