This project concerns the frontiers of fundamental physics. It is composed of two sides: (I) research on the quantum-gravity problem, the problem that marks the utmost frontier of fundamental physics, where general relativity and quantum mechanics should unite, and (II) the organization of a conference and work on an edited book collecting the views of leading physicists and philosophers of science concerning whether or not it could be possible to find a 'theory of everything'. The two sides of the project are connected: my approach to the study of the quantum-gravity problem is alternative to the methodologies of the mainstream approaches to the quantum-gravity problem, indeed because I do not assume that the correct quantum gravity should be a 'theory of everything'. The approach adopted for the quantum-gravity-research side of this project assumes that any physical theory must be inevitably incomplete, limited to providing partial answers to only some of the questions, and in turn this renders inevitable that we should face the challenge of seeking experimental confirmation of the very tiny effects expected from quantum gravity. The main focus will be on developing theoretically and exploiting phenomenologically some recent results showing that the unification of general relativity and quantum mechanics may require a revision of the relativity postulates. This involves the notion of 'relative locality', which must be accommodated within the relativistic framework, attributing to it no less significance than the notion of 'relative simultaneity' which is the cornerstone of the relativity revolution of about a century ago championed by Einstein. These quantum-gravity scenarios hosting 'relative locality' are expected to produce testable predictions for the observation of particles that reach our observatories from cosmological distances. These predictions will be derived in detail and a phenomenological program based on them will be proposed.