XQuery is a W3C standard language which is meant to be for XML what SQL is for relational data--i.e., the ability to search, sort, extract, and remold data. It offers powerful and yet intuitive searching based on XPath, has SQL-like syntax for the query portion, and has scripting features such as function and variable definitions, XML-inclusion, etc.
XqUSEme (registration required as extension is still under review) is a proof-of-concept (presently Windows-only) extension which allows one to perform XQueries on external URL's, the currently loaded webpage (even if originally from poorly formed HTML), and/or XML (including well-formed XHTML) documents stored locally.
While an implementation could be envisioned which did not have the (large) overhead of a database system (e.g., by interfacing with the open-source version of Saxonica's Saxon B), a database system has the advantage of allowing local storage and indexing. Other popular native XML databases might also be supported (e.g., eXist), especially with an open-standard (XQJ) for Java apparently around the corner, but Berkeley DB XML was chosen by the extension developer for its support across many languages (C++, Java, Python, Perl, PHP, etc.) (besides being open source).
At present, the extension works simply by using LiveConnect to work with Berkeley DB XML's Java API (and via a Java wrapper class which circumvents LiveConnect's inability to handle some types of Java exceptions properly). However, use of the approach of the Java Firefox extension might be used to turn the above extension concept into an XPCOM component (giving it access to all open windows), and possibly implementing it in C++ instead, which is the database's original language of development.