This chapter argues that a knowledge discovery system should be interactive, should utilise the best in artificial intelligence (AI), evolutionary, and statistical techniques in deriving results, but should be able to trade accuracy for understanding. Further, it needs to provide a means for users to indicate what exactly constitutes “interesting”, as well as understanding suggestions output by the computer. One such system is Haiku, which combines interactive 3D dynamic visualization and genetic algorithm techniques, and enables users to visually explore features and evaluate explanations generated by the system. Three case studies are described which illustrate the effectiveness of the Haiku system, these being Australian credit card data, Boston area housing data, and company telecommunications network call patterns. We conclude that a combination of intuitive and knowledge-driven exploration, together with conventional machine learning algorithms, offers a much richer environment, which in turn can lead to a deeper understanding of the domain under study.