What is reduction? Must all discussions of the mind, value, colour, biological organisms, and persons aim to reduce these to objects and properties that can be studied by more basic, physical science? Conversely, does failure to achieve a reduction undermine the legitimacy of higher levels of description or explanation? In recent years philosophers have attempted to avoid these traditional alternatives by developing an account of higher-level phenomena which shows them to be grounded in, but not reducible to, basic physical objects and properties. The contributors to this volume examine the motivations for such anti-reductionist views, and assess their coherence and success, in a number of different fields. Their essays constitute a unified discussion, into which the reader is led by an introductory chapter where the editors set out some of the central claims and questions.