In this paper, we discuss the problem of organizing the different ways of computing the interestingness of a particular cell derived from a cube in the context of a hierarchical, multidimensional space. We start from an in-depth study of the interestingness aspects in the study of human behavior and include in our survey the approaches taken by computer-science efforts in the area of data mining and user recommendations. We move on to structure interestingness along different fundamental, high level aspects, and, due to their high-level nature, we also move towards much more concrete data-oriented definitions of intertestingness aspects.