Analysts predominantly use OLAP data cubes to identify regions of anomalies that may represent problem areas or new opportunities. The current OLAP systems support hypothesis-driven exploration of data cubes through operations such as drill-down, roll-up, and selection. Using these operations, an analyst navigates unaided through a huge search space looking at large number of values to spot exceptions. We propose a new discovery-driven exploration paradigm that mines the data for such exceptions and summarizes the exceptions at appropriate levels in advance. It then uses these exceptions to lead the analyst to interesting regions of the cube during navigation. We present the statistical foundation underlying our approach. We then discuss the computational issue of finding exceptions in data and making the process efficient on large multidimensional data bases.