This essay surveys the main objections to aesthetic hedonism, the view that aesthetic value is reducible to the value of aesthetic pleasure or experience. Hedonism is the dominant view of aesthetic value, but a spate of recent criticisms has drawn its accuracy into question. I introduce some distinctions crucial to the criticisms, before using the bulk of the essay to identify and review six major lines of argument that hedonism's critics have employed against it. Whether or not these arguments suffice to refute hedonism decisively, I argue that its privileged status, as the sole contender in aesthetic value theory, is detrimental to downstream research on aesthetic phenomena. The essay concludes with an overview of current work and promising avenues of inquiry into non-hedonic alternatives.