This article explores the relationship and disparities between human and computational creativity by addressing the following questions: How well are computational creativity systems currently performing at creative tasks? Could computers outperform human composers? And, if not, is computational creativity a utopia? Automatic composition systems are examined with respect to Boden’s three criteria of creativity (novelty, surprise and value), as well as their assumptions about the nature of creativity. As an alternative to a competitive relationship between human and computational creativity, the article proposes the concept of a distributed human–computer co-creativity, in which computational creativity extends – rather than replaces – human creativity, by expanding the space of creative possibilities.