We discuss the complexity of enumerating (listing) the answers to a query over a relational database. We focus on the ability to list the answers with linear preprocessing and constant time per answer. A known dichotomy classifies Conjunctive Queries (CQs) into those that admit such enumeration and those that do not. I will talk about our research towards extending this dichotomy to the class of Unions of CQs (UCQs). A union of tractable CQs is always tractable. We show that, counter to previous beliefs, some non-redundant unions containing intractable CQs are tractable. Interestingly, some unions consisting of only intractable CQs are tractable too. The question of finding a full characterization of the tractability of UCQs remains open.