Publisher Summary This chapter discusses the topic of creativity related to the field of artificial intelligence (AI). In addition to the ambiguities regarding product, process, or person, the definition of creativity is problematic for four reasons. The first problem is that positive evaluation is essential to the concept. An idea counted as creative must be interesting. This judgment often rests on social and historical factors, and no purely psychological theory could explain these evaluations. The second problem concerns the question whether the originator must recognize the value of an idea for it to be called creative. If so, then someone who has a good idea but rejects it as uninteresting is not creative. The third difficulty is the tension between psychological (P) and historical (H) senses. An idea is P-creative if it is creative with respect to the mind of the person concerned, even if others have had that idea already. An idea is H-creative if it is P-creative and no other person has had the idea before. H-creativity is more glamorous, but P-creativity is more fundamental. The fourth problem is that the familiar operational definition fits only some cases. Many psychologists define creativity as the novel combination of familiar ideas. This does not distinguish P-novelty from H-novelty nor does it mention evaluation. Therefore, two definitions of creativity are needed, both requiring that the novel idea be interesting. Improbabilist creativity concerns novel and improbable combinations of familiar ideas. Impossibilist or exploratory-transformational creativity concerns novel ideas that, relative to the pre-existing conventions of the domain, the person could not have had before. This chapter describes both these types of creativity and discusses AI models related to arts and science. The chapter closes with a discussion on self-transforming programs such as (Automatic Mathematician) AM and Eurisko.