We find “vertical” relations in many different realms, whether between atoms and molecules, words and sentences, neurons and brains, or individuals and societies. This book is the first to bring together, and comparatively assess, the exciting array of philosophical approaches to vertical relations that have independently sprung up in analytic metaphysics, the metaphysics of mind, and the philosophy of science.  Analytic metaphysicians have recently focused on a relation of ‘Ground’ that is claimed to be found in aesthetics, ethics, logic, mathematics, science, and semantics.  Metaphysicians of mind have focussed on a vertical relation of ‘realization’ between properties, whilst philosophers of science associated with the rise of the ‘New Mechanism’ have renewed interest in vertical relations of scientific composition found in so-called “mechanistic explanations”. This volume analyses the inter-relations between these different approaches to spark a range of new debates, including whether the various frameworks for vertical relations are independent, complementary or in even competition.