Reactivity, the ability to detect and react to events, is an essential functionality in many information systems. In particular, Web systems such as online marketplaces, adaptive (e.g., recommender) systems, and Web services, react to events such as Web page updates or data posted to a server. This article investigates issues of relevance in designing high-level programming languages dedicated to reactivity on the Web. It presents twelve theses on features desirable for a language of reactive rules tuned to programming event-driven Web and Semantic Web applications. an extended abstract of a talk given during the Dagstuhl Seminar "Event Processing." A longer version of this work, which explains and justifies each thesis in detail, has been presented with the same title at the workshop "Reactivity on the Web" at EDBT 2007, see [1].