Data Mining has evolved as a new discipline at the intersection of several existing areas, including Database Systems, Machine Learning, Optimization, and Statistics. An important question is whether the field has matured to the point where it has originated substantial new problems and techniques that distinguish it fromits parent disciplines. In this paper, we discuss a class of new problems and techniques that show great promise for exploratory mining, while synthesizing and generalizing ideas from the parent disciplines. While the class of problems we discuss is broad, there is a common underlying objective-to look beyond a single data mining step (e.g., data summarization or model construction) and address the combined process of data selection and transformation, parameter and algorithm selection, and model construction. The fundamental difficulty lies in the large space of alternative choices at each step, and good solutions must provide a natural framework for managing this complexity. We regard this as a grand challenge for DataMining, and see the ideas in this paper as promising initial steps towards a rigorous exploratory framework that supports the entire process.