The problem of intentional inexistence arises because the following (alleged) intuitions are mutually conflicting: it seems that sometimes we think about things that do not exist; it seems that intentionality is a relation between a thinker and what such a thinker thinks about; it seems that relations entail the existence of what they relate. In this paper, I argue for what I call a radical relationist solution. First, I contend that the extant arguments for the view that relations entail the existence of their relata are wanting. In this regard, I defend a kind of pluralism about relations according to which more than one kind of relation involves non-existents. Second, I contend that there are reasons to maintain that all thoughts are relations between thinkers and the things they are about. More accurately, I contend that the radical relationist solution is to be preferred to both the intentional content solution (as developed by Crane) and the adverbial property solution (as developed by Kriegel). Finally, I argue that once the distinction between thinking “X” and thinking about X has been drawn, the radical relationist solution can handle issues like ontological commitment, substitutivity failure, scrutability, and non-specificity.