Are there truly fundamental entities in nature? Or are the things that we regard as fundamental in our theories - for example space, time or the masses of elementary particles - merely awaiting a derivation from a new, yet to be discovered theory based on elements that are more fundamental? This was the central question posed in the 2018 FQXi essay competition, which drew more than 200 entries from professional physicists, philosophers, and other scholars. This volume presents enhanced versions of the fifteen award-winning essays, giving a spectrum of views and insights on this fascinating topic. From a prescription for when to stop digging to the case for strong emergence, the reader will find here a plethora of stimulating and challenging ideas - presented in a largely non-technical manner - on which to sharpen their understanding of the language of physics and even the nature of reality.