The (im)moral character of art works often affects how we respond to them. But should it affect our evaluation of them as art? The article surveys the contemporary debate whilst outlining further lines of argument and enquiry. The main arguments in favour of aestheticism, the claim that there is no internal relation between artistic value and moral character, are considered. Nonetheless the connection between art's instructional aspirations and artistic value, as well as the ways in which works solicit responses from us, underwrite the claim that a work's moral character can be directly relevant to a work's value as art. Various competing accounts of how the relationship goes, ethicism, moderate moralism and immoralism, are considered. The article goes on to elaborate novel considerations in favour of a suitably qualified cognitive immoralism and suggests avenues of further enquiry with respect to the moral character of art works.