What is fundamental 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 Introduction Fundamental (Emily Adlam) Against Fundamentalism (Matthew Leifer) The Politics of Fundamentality (Alyssa Ney) Of Lego and Layers (and Fundamentalism) (Dean Rickles) Fundamentality Here Fundamentality There Fundamentality Everywhere (Marc Séguin) Mind before matter: reversing the arrow of fundamentality (Markus Müller) Things Laws and the Human Mind (Tejinder Singh) The Case for Strong Emergence (Sabine Hossenfelder) Mad Dog Everettianism: Quantum Mechanics at Its Most Minimal (Sean Carroll Ashmeet Singh) Bells Theory of Beables and the Concept of Universe (Ian Durham) Fundamentality Explanation and the Unity of Science (Gregory Derry) When do we stop digging Conditions on a fundamental theory of physics (Karen Crowther) Fundamental is Non Random (Ken Wharton) Socrates Atoms and Beig: A Dialogue (Mozibur Ullah).Fundamentality as a Linguistic Paradigm (and Linguistics as a Fundamental Paradigm) (Aditya Dwarkesh)