This paper structures a novel vision for OLAP by fundamentally redefining several of the pillars on which OLAP has been based for the last 20 years. We redefine OLAP queries, in order to move to higher degrees of abstraction from roll-up's and drill-down's, and we propose a set of novel intentional OLAP operators, namely, describe, assess, explain, predict, and suggest, which express the user's need for results. We fundamentally redefine what a query answer is, and escape from the constraint that the answer is a set of tuples; on the contrary, we complement the set of tuples with models (typically, but not exclusively, results of data mining algorithms over the involved data) that concisely represent the internal structure or correlations of the data. Due to the diverse nature of the involved models, we come up (for the first time ever, to the best of our knowledge) with a unifying framework for them, that places its pillars on the extension of each data cell of a cube with information about the models that pertain to it -- practically converting the small parts that build up the models to data that annotate each cell. We exploit this data-to-model mapping to provide highlights of the data, by isolating data and models that maximize the delivery of new information to the user. We introduce a novel method for assessing the surprise that a new query result brings to the user, with respect to the information contained in previous results the user has seen via a new interestingness measure. The individual parts of our proposal are integrated in a new data model for OLAP, which we call the Intentional Analytics Model. We complement our contribution with a list of significant open problems for the community to address.