The world we live in is a rich and varied place. It contains such diverse things as elementary particles and magnetic fields, mass demonstrations and the French nation, Socrates paleness, his unit set and the primary colours. But, arguably, these items are not all on a par. Rather, the world around us exhibits significant structure: some features are more fundamental than others, some phenomena depend on other phenomena, and certain things exist only because others do. This collection focusses on four notions that have been used to formulate such metaphysical claims about the structure of the world: ontological dependence, grounding, supervenience, and response dependence. For each of these notions, it includes state of the art survey papers introducing the reader to the relevant issues, concepts and distinctions as well as original research papers by leading researchers in their fields. The collection thus aims both at the novice reader interested in this exciting and quickly developing part of metaphysics as well as the expert looking for original contributions that advance the state of debate.