This paper joins recent attempts to defend a notion of aesthetic experience. It argues that phenomenological facts and facts about aesthetic value support the Kantian notion that aesthetic experience lies between, but differs from, pleasures of the agreeable and pleasures stemming from cognitions. It then shows that accounts by Beardsley, Levinson, and Savile fail to resolve clear tensions that surface in attempting to characterize such an experience. An account of aesthetic experience—as involving experienced cognitions that are the bearers of value—is presented. The paper ends on a sceptical note as to whether aesthetic experience can be clearly delimited.