Concessive knowledge attributions (CKAs) are knowledge attributions of the form ‘S knows p, but it’s possible that q’, where q obviously entails not-p (Rysiew, Nous (Detroit, Mich.) 35:477–514, 2001). The significance of CKAs has been widely discussed recently. It’s agreed by all that CKAs are infelicitous, at least typically. But the agreement ends there. Different writers have invoked them in their defenses of all sorts of philosophical theses; to name just a few: contextualism, invariantism, fallibilism, infallibilism, and that the knowledge rules for assertion and practical reasoning are false. In fact, there is a lot of confusion about CKAs and their significance. I try to clear some of this confusion up, as well as show what their significance is with respect to the debate between fallibilists and infallibilists about knowledge in particular.