The peer-to-peer computing paradigm is an intriguing alternative to Google-style search engines for querying and ranking Web content. In a network with many thousands or millions of peers the storage and access load requirements per peer are much lighter than for a centralized Google-like server farm; thus more powerful techniques from information retrieval, statistical learning, computational linguistics, and ontological reasoning can be employed on each peer¢s local search engine for boosting the quality of search results. In addition, peers can dynamically collaborate on advanced and particularly difficult queries. Moroever, a peer-to-peer setting is ideally suited to capture local user behavior, like query logs and click streams, and disseminate and aggregate this information in the network, at the discretion of the corresponding user, in order to incorporate richer cognitive models. This paper gives an overview of ongoing work in the EU Integrated Project DELIS that aims to develop foundations for a peer-to-peer search engine with Google-or-better scale, functionality, and quality, which will operate in a completely decentralized and self-organizing manner. The paper presents the architecture of such a system and the Minerva prototype testbed, and it discusses various core pieces of the approach: efficient execution of top-k ranking queries, strategies for query routing when a search request needs to be forwarded to other peers, maintaining a self-organizing semantic overlay network, and exploiting and coping with user and community behavior.