Since Premack and Woodruff's classic (1978) paper, the term ‘theory of mind’ has come to designate a particular research-domain, whose goal is to provide an explanation of the ability – which may or may not be unique to human beings – to explain and predict the actions, both of oneself, and of other intelligent agents. It is also the term used to designate one controversial characterisation of the basis of this ability. So-called ‘theory-theorists’ maintain that the ability to explain and predict behaviour is underpinned by a folk-psychological theory of the structure and functioning of the mind – where the theory in question may be innate and modularised, learned individually, or acquired through a process of enculturation. There are, then, many different theories of theory of mind in its research-domain sense; and the theory-theory account of our theory of mind abilities, too, admits of a number of different variants. Moreover, both sets of questions are now of common concern to a number of different disciplines, including philosophy, primatology, cognitive science, and developmental psychology. These multiplicities are reflected in the title of this volume, and in its contents. In this brief introductory chapter we shall provide the reader with a map of the area, laying out the issues and options, and linking these to the chapters that follow.