In this paper, we discuss methods to assess the interestingness of a query in an environment of data cubes. We assume a hierarchical multidimensional database, storing data cubes and level hierarchies. We start with a comprehensive review of related work in the fields of studies of human behavior and computer science. We define the interestingness of a query as a vector of scores along difference dimensions, like novelty, relevance, surprise and peculiarity and complement this definition with a taxonomy of the information that can be used to assess each of these dimensions of interestingness. We provide both syntactic (result-independent) checks and extensional (result-dependent) measures and algorithms for assessing the different dimensions of interestingness in a quantitative fashion. We also report our findings on a user study that we conducted, analyzing the significance of each dimension, its evolution over time and the behavior of the study's participants.