Notions relating to computational systems exhibiting creative behaviours have been explored since the very early days of computer science, and the field of Computational Creativity research has formed in the last dozen years to scientifically explore the potential of such systems. We describe this field via a working definition; a brief history of seminal work; an exploration of the main issues, technologies and ideas; and a look towards future directions. As a society, we are jealous of our creativity: creative people and their contributions to cultural progression are highly valued. Moreover, creative behaviour in people draws on a full set of intelligent abilities, so simulating such behaviour represents a serious technical challenge for Artificial Intelligence research. As such, we believe it is fair to characterise Computational Creativity as a frontier for AI research beyond all others—maybe, even, the final frontier.