The current search engine model considers users not trustworthy, so no tools are provided to let them specify what they are looking for or in what context, which severely limits what they are able to achieve. Instead, search engines try to guess that, which is currently done using "implicit feedback''. In this paper we propose a "web exploration engine'' - a model where users can use the search engine as their tool and explicitly specify the context of their search. Information about the web has been pre-classified in a large number of categories; users can explore this hierarchy by providing relevance feedback or search within a particular category. Search is truly ``local'' in the sense that keyword relevance is not global, but specific to the category. In contrast to using a search engine, users can guide the exploration engine with relevance feedback alone without entering keywords.