"Complexity sciences" are an interdisciplinary and transnational domain of study that aims at modeling natural and social "complex systems." They appeared in the 1970s in Europe and the United States, but were boosted in the mid-1980s by the Santa Fe Institute (SFI) under the formula of "science of complexity." This small but famous institution is the object of the present article. According to their promissory ambitions and to the enthusiastic claims of some scientific journalists, complexity sciences were going to revolutionize all of knowledge and even private and public actors who had learned to master them. In the light of this, one would expect to observe a well-established and autonomous research and educational field, capable of reproducing itself through professional institutions. Yet this is not the case. To explain the paradox, I propose to combine different models of history and sociology of emergent and declining domains, in order to give account of the rise and failure of complexity sciences.