A major question for linguistic theory concerns how the structure of sentences relates to their meaning. There is broad agreement in the field that there is some regularity in the way that lexical semantics and syntax are related, so that thematic roles are predictably associated with particular syntactic positions. This book examines the syntax and semantics of possession sentences, which are infamous for appearing to diverge dramatically from this broadly regular pattern. On the one hand, possession sentences have too many meanings: in a given language, the construction used to express archetypal possessive meanings (such as personal ownership) is also often used to express other apparently unrelated notions (body parts, kinship relations, and many others). On the other hand, possession sentences have too many surface structures: languages differ markedly in the argument structures used to convey the same possessive meanings, with some employing a transitive verb HAVE, and others using a variety of constructions based around an intransitive verb BE. Examining and synthesizing ideas from the literature and drawing on data from many languages (including some understudied Quechua dialects), this book presents a novel way to understand the apparent irregularity of possession sentences while preserving existing explanations for the general cross-linguistic regularities we observe in argument structure.