The envisioned Semantic Web aims to provide richly annotated and explicitly structured Web pages in XML, RDF, or description logics, based upon underlying ontologies and thesauri. Ideally, this should enable a wealth of query processing and semantic reasoning capabilities using XQuery and logical inference engines. However, we believe that the diversity and uncertainty of terminologies and schema-like annotations will make precise querying on a Web scale extremely elusive if not hopeless, and the same argument holds for large-scale dynamic federations of Deep Web sources. Therefore, ontology-based reasoning and querying needs to be enhanced by statistical means, leading to relevanceranked lists as query results. This paper presents steps towards such a “statistically semantic” Web and outlines technical challenges. We discuss how statistically quantified ontological relations can be exploited in XML retrieval, how statistics can help in making Web-scale search efficient, and how ...