Can we imagine the impossible? While the impossibilists give an affirmative answer to this question, the anti-impossibilists claim that imagination is limited to the possible and correspondingly deny that impossibilities are imaginable. My own sympathies lie with the former camp, and the aim of this paper is to make the case for impossibilism. The discussion proceeds in roughly three stages. In Section 1, I clarify the debate. This consists of two main tasks: elucidating the notion of impossibility involved and elucidating what imagination is and how it differs from other speculative states like supposition. In Section 2, I consider what I call the appeal to introspection, the key move often made by the anti-impossibilist in defending their position, and I aim to show why this appeal should be rejected. In Section 3, I turn more directly to a defense of impossibilism. As we will see, the defense requires the impossibilist to explain how impossibilities might be imagined. After first discussing two impossibilist strategies that I think turn out to be unsuccessful, I then turn to two more promising strategies: what I call the pathway strategy and what I call the disguise strategy.