We summarize in this introduction the contents of all the contributions included in Synthese special issue on form, structure and hylomorphism. Moreover, we provide an exhaustive bibliography of recent research on these topics. Keywords Form • Structure • Hylomorphism Providing a brief and uncontroversial introduction to the metaphysical theory known as hylomorphism (from the Greek hyle matter, and morphé form) is a nearly impossible task, on account of the multiplicity of existing interpretations of Aristotle's original view, and also of the ways his view has been developed, starting with his own immediate commentators. Roughly speaking, hylomorphism is the metaphysical position according to which objects have a "formal" as well as a "material" "component". The philosophical meaning of each of these terms is controversial. In lieu of any inevitably biased account of what these terms refer to, we will here only try to help the reader explore further, with a selected bibliography in appendix. In this special issue, we have collected papers that develop contemporary versions of hylomorphism, and explore some of its applications. One (even if not the only) dimension along which contemporary hylomorphist accounts differ concerns which types of entity they posit to do the metaphysical work they take an Aristotelian form to do: structures; relations; powers; functions; special sorts of components of complex entities; or sui generis entities-this list is far from being exhaustive. Another dimension concerns the way matter and form are unified and give rise to an hylomorphic compound. A further dimension regards the philosophical consequences of adopting