We call data intensional when it is not directly available, but must be accessed through a costly interface. Intensional data naturally arises in a number of Web data management scenarios, such as Web crawling or ontology-based data access. Such scenarios require us to model an uncertain view of the world, for which, given a query, we must answer the question “What is the best thing to do next?” Once data has been retrieved, the knowledge of the world is revised, and the whole process is repeated, until enough knowledge about the world has been obtained for the particular application considered. In this article, we give an overview of the steps underlying all intensional data management scenarios, and illustrate them on three concrete applications: focused crawling, online influence maximization in social networks, and mining crowdsourced data.