Condensed representations have been proposed in Mannila and Toivonen (1996) as a useful concept for the optimization of typical data-mining tasks. It appears as a key concept within the inductive database framework (Boulicaut et al., 1999; de Raedt, 2002; Imielinski & Mannila, 1996), and this article introduces this research domain, its achievements in the context of frequent itemset mining (FIM) from transactional data, and its future trends.