Abstract: Consider the following claim: my attempts at squaring the circle failed because squaring the circle is (mathematically) impossible. According to some this is a genuine explanation while others deny this. One particularly interesting way of denying that there is an explanation here is offered by our own Nick Smith, who claims that what we have in such cases is the end of explanation and this should not be confused with an explanation. One motivation for such a view comes from counterfactual accounts of explanation. According to such accounts, we look for the nearest possible world in which the circle can be squared and check whether my attempts succeed there. But because there is no possible world in which the circle can be squared, we do not have an explanation. In short, counterfactual accounts of explanation do not permit impossibilities as explanations. There is, however, a natural extension of counterfactual accounts of explanation that allow counterpossibles (and hence impossible worlds). Such accounts do deliver the result that impossibilities can be explanatory. For some this is a welcome result but it comes with a challenge. Once we allow impossible worlds we need a substantive account of why impossibilities are never actualised (e.g. why the impossible world where the circle is squared is not the actual world). In this paper I will discuss this challenge and defend the counterpossible account of explanation.