As Deleuze scholars, or as philosophers seeking to apply his philosophical insights in various domains, we sometimes speak and write as though Deleuze's concepts were well understood. When we examine the literature, however, we find a surprising lack of consensus regarding the sense of his core concepts, even those as central as the virtual, the actual and the intensive. To take the concept of intensity as a significant example, commentators seem to be divided as to: whether the intensive is virtual in nature or whether it constitutes a third ontological realm; the proximity of the philosophical conception of intensity to the scientific one; the philosophical work which this concept is tasked with at different points in Deleuze's oeuvre; and who the key thinkers are without whom Deleuze would not have been able to articulate his conception(s) of intensity. It is with an eye to these discordances that the present special issue has been assembled. We have not proposed to resolve them. Quite the contrary, we have wished to emphasize them. Each of the authors contributing to this special issue thus problematize in novel ways our ordinary understanding of the sense and status of the concepts of the virtual, the actual and the intensive, and collectively open up a problematic space in which we might think them anew.