In many internet applications, such as web searches, contexts are important because each search is done with a specific context in mind, and results outside that context are seen by the user as irrelevant. By measuring joint keyword occurrences in web pages, around our notion of "Semantic Contexts" we propose an infrastructure for semantically characterizing contextual information in the internet. Semantic Contexts could have many practical uses, such as focusing internet searches in such a way that results would be much more relevant to users than with current search engines. Semantic Contexts could also be linked to Semantic Web definitions, such as ontologies, giving a way to leverage the currently marginal Semantic Web.