We consider the problem of handling "similarity queries" in peer-to-peer databases. Given a query for a data object, we propose an indexing and searching mechanism which returns the set of objects in the database that are semantically related to the query. Our schemes can be implemented on a variety of structured overlays such as CAN, CHORD, Pastry, and Tapestry. We provide analytical and experimental evaluation of our schemes in terms of the search accuracy, search cost, and load balancing. Our analytical guarantees perfectly predict the experimentally observed trends for the search accuracy.