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The present chapter deals with some general issues of an epistemological nature concerning the notion of complexity. Such issues are examined here only informally. Moreover, there will be no impassioned stance (a few personal remarks will be confined to footnotes), but only conceptual analysis. Its motivation hinges on the increasing use of the notion of complexity in social sciences, as if it had one definite meaning, whereas such a meaning is hard to find. Consequently, the expected benefits of its application within the social sciencesbring a growing risk of ambiguity, which hinders the establishment of solid grounds on which to test the use of the notion and evaluate its contribution to the advance of knowledge.To reduce this risk, the manifold faces of complexity will be considered, not so much in a mathematical setting but by going back to a list of seminal works to which its current uses are in debt. Some of these works offered an exact formulation, some did not; together they gave rise to lines of research which are still far from convergence on a common theory. The present analysis provides warnings against excessive expectations and abuses of the notion resting on an appeal to rhetoric and aims to provide a step towards clarifying the scientific meaning of complexity.

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