Since Antiquity, logic has always enjoyed a status of something crucially important, because it shows us how to reason, if we are to reason correctly. Yet the twentieth century fostered an unprecedented boost in logical studies and delivered a wealth of results, most of which are not only not understandable by non-specialists, but their very connection with the original agenda of logic is far from clear. In this paper, I survey how the achievements of modern logic are construed by non-specialists and subject their construals to critical scrutiny. I argue that logic cannot be taken as a theory of the limits of our world and that its prima facie most plausible construal as a theory of reasoning is too unclear to be taken at face value. I argue that the viable construal of logic takes it to be explicative of the constitutive (rather than strategic) rules of reasoning, not of the rules that tell us how to reason, but rather of rules that make up the tools with which (or in terms of which) we reason.