Many areas of language-related research -- language processing, linguistic semantics/pragmatics, speech understanding and synthesis, and psychological theories of attention -- have shown an increasing need to describe and understand aspects of discourse anaphora in relation to both processing complexity and the global structure of discourse. A major problem in this area is the large gap between existing theories and accounts of actual phenomena in naturally occurring discourse. Centering Theory is an account of one aspect of discourse, local discourse structure, that makes specific claims about both processing complexity and discourse anaphora. Centering Theory in Discourse focuses on Centering Theory's ability to account for data from naturally occurring discourse in several languages. The contributors test empirically several claims of Centering Theory, propose extensions to and refinements of Centering, and show how it can be integrated with other aspects of discourse structure and processing.