The languages of the small Nyulnyulan family of the far northwest of Western Australia all exhibit a grammatical category traditionally dubbed irrealis. In this paper we describe the grammatical expression of this category, and its range of meanings and uses. It is argued that these can be accounted for as contextual senses or pragmatic inferences based on a single encoded core meaning, that the referent situation is construed by the speaker as unrealized. This semantic component remains invariant across all uses of the category, and is not defeasible. Contra claims by some investigators, the realis-irrealis mood contrast is fundamental, and encapsulates a viable conceptual contrast between real and unreal events; epistemic and deontic notions of probability, necessity, desirability, and the like are secondary pragmatic inferences. The irrealis is thus a modal category that can grammaticalize in human languages; indeed, it is a communicatively useful category. We explicate the nature of the conceptual contrast between the construed real and unreal. It is further argued that the notion of scope is essential to an understanding of the irrealis, and its interaction with other mode-like categories. Finally, we situate the Nyulnyulan irrealis in the wider cross-linguistic context of irrealis.