Interactive art has become much more common as a result of the many ways in which the computer and the Internet have facilitated it. Issues relating to Human-Computer Interaction are as important to interactive art making as issues relating to the colours of paint are to painting. It is not that HCI and art necessarily share goals. It is just that much of the knowledge of HCI and its methods can contribute to interactive art making. This paper reviews recent work that looks at these issues in the art context. In interactive digital art, the artist is concerned with how the artwork behaves, how the audience interacts with it and, ultimately, in participant experience and their degree of engagement. The paper looks at these issues and brings together a collection of research results and art practice experiences that together help to illuminate this significant new and expanding area. In particular, it is suggested that this work points towards a much needed critical language that can be used to describe, compare and discuss interactive digital art.