This book is about one of the most intriguing features of human communication systems: the fact that words which go together in meaning can occur arbitrarily far away from each other. The kind of long-distance dependency that this volume is concerned with has been the subject of intense linguistic and psycholinguistic research for the last half century, and offers a unique insight into the nature of grammatical structures and their interaction with cognition. The constructions in which these unbounded dependencies arise are difficult to model and come with a rather puzzling array of constraints which have defied characterization and a proper explanation. For example, there are filler-gap dependencies in which the filler phrase is a plural phrase formed from the combination of each of the extracted phrases, and there are filler-gap constructions in which the filler phrase itself contains a gap that is linked to another filler phrase. What is more, different types of filler-gap dependency can compound, in the same sentence. Conversely, not all kinds of filler-gap dependencies are equally licit; some are robustly ruled out by the grammar whereas others have a less clear status because they have graded acceptability and can be made to improve in ideal contexts and conditions. This work provides a detailed survey of these linguistic phenomena and extant accounts, while also incorporating new experimental evidence to shed light on why the phenomena are the way they are and what important research on this topic lies ahead.