Disambiguating concepts and entities in a context sensitive way is a fundamental problem in natural language processing. The comprehensiveness of Wikipedia has made the online encyclopedia an increasingly popular target for disambiguation. Disambiguation to Wikipedia is similar to a traditional Word Sense Disambiguation task, but distinct in that the Wikipedia link structure provides additional information about which disambiguations are compatible. In this work we analyze approaches that utilize this information to arrive at coherent sets of disambiguations for a given document (which we call “global” approaches), and compare them to more traditional (local) approaches. We show that previous approaches for global disambiguation can be improved, but even then the local disambiguation provides a baseline which is very hard to beat.