Disfluencies include editing terms such as uh and um as well as repeats and revisions. Little is known about how disfluencies are processed, and there has been next to no research done to address the way that disfluencies affect structure-building operations during comprehension. I will describe our own work which examines how the parser behaves when it encounters a disfluency. I will also present a preliminary model of disfluency processing which assumes that a Tree Adjoining Grammar builds phrase structure. On this approach, filled and unfilled pauses affect the timing of Substitution operations. Repairs and corrections are handled by a mechanism we term "Overlay", which allows the parser to overwrite an undesired tree with the appropriate, correct tree. This model highlights the need for the parser to sometimes coordinate the mechanisms that perform garden-path reanalysis with those that do disfluency repair. The research program as a whole demonstrates that it is possible to study disfluencies systematically and to learn how the parser handles filler material and mistakes. It also showcases how elegantly Tree Adjoining Grammars capture many aspects of human language performance.