Abstract Many experts predict that the next huge step forward in Web information technology will be achieved by adding semantics to Web data, and will possibly consist of (some form of) the Semantic Web. In this paper, we present a novel approach to Semantic Web search, called Serene, which allows for a semantic processing of Web search queries, and for evaluating complex Web search queries that involve reasoning over the Web. More specifically, we first add ontological structure and semantics to Web pages, which then allows for both attaching a meaning to Web search queries and Web pages, and for formulating and processing ontology-based complex Web search queries (i.e., conjunctive queries) that involve reasoning over the Web. Here, we assume the existence of an underlying ontology (in a lightweight ontology language) relative to which Web pages are annotated and Web search queries are formulated. Depending on whether we use a general or a specialized ontology, we thus obtain a general or a vertical Semantic Web search interface, respectively. That is, we are actually mapping the Web into an ontological knowledge base, which then allows for Semantic Web search relative to the underlying ontology. The latter is then realized by reduction to standard Web search on standard Web pages and logically completed ontological annotations. That is, standard Web search engines are used as the main inference motor for ontology-based Semantic Web search. We develop the formal model behind this approach and also provide an implementation in desktop search. Furthermore, we report on extensive experiments, including an implemented Semantic Web search on the Internet Movie Database.