Despite decades of challenges to the idea that a small number of emotions enjoys the special status of “basic emotions,” the idea continues to have considerable influence in psychology and beyond. However, different theorists have proposed substantially different lists of basic emotions, which suggests that there exists no stable criterion of basicness. To some extent, the basic-emotions enterprise is bedeviled by an overreliance on English affective terms, but there also lurks a more serious problem—the lack of agreement as to what emotions are. To address this problem, three necessary conditions are proposed as a minimal requirement for a mental state to be an emotion. A detailed analysis of surprise, a widely accepted basic emotion, reveals that surprise violates even this minimal test, raising the possibility that it and perhaps other would-be basic emotions might not be emotions at all. An approach that combines ideas such as undifferentiated affect and cognitive appraisal is briefly proposed as a way of theorizing about emotions that is less dependent on the vagaries of language and incoherent notions of basic emotions. Finally, it is suggested that the perennial question of what an emotion is should be given more serious attention.