This introductory article outlines the central topic of the present special issue, viz. the contrast between alienable and inalienable possession, and how this contrast is reflected in the grammars and lexicons of natural languages. It sketches the historical background of the alienability contrast in the linguistic literature and points to a number of biases that need to be overcome in order to (1) advance our understanding of the contrast and (2) face the limits of its explanatory potential. Specifically, the present introduction, as well as the contributions to the present issue, proposes to move beyond prototypical possessive relationships (ownership, part-whole, and kinship relations), prototypical possessor categories (human possessors) as well as prototypical possessee categories (artifacts, body-parts and kin). In addition, the issue contains three contributions dealing with Amazonian languages, thus filling in an important gap in previous crosslinguistic studies on possession. The data presented in the special issue show that many morphosyntactic phenomena that have been explained in terms of the alienability contrast – or are amenable to such explanations – cannot be reduced to it, and are sometimes even better described without recourse to alienability at all. The present article thus concludes that the alienability contrast is at best regarded as a heuristic tool in exploring linguistic data, and cautions that, if used as the only explanatory principle, it could actually hamper an adequate description of the data.