Book excerpt: The present volume of Time and Science series is devoted to Physical Sciences and Cosmology. Today more than ever, the question 'is Time an ontological property, a necessary ingredient for the physical description of the world, or a purely epistemological element, relative to our situation in the world?' worry physicists and cosmologists alike. For many of them, Relativity (and particularly General Relativity), as well as its reconciliation with quantum mechanics in the elaboration of a quantum theory of gravitation, points to a negative answer to the first alternative, and leads them to deny the objective reality of time. For others, the answer is nuanced by the evidence of an emerging temporal property when one climbs the scales of the complexity of systems and/or the applicability of the statistical laws of thermodynamics. But for some, the illusion of the unreality of time comes from certain confusions that they denounce, and plead for the re-establishment of time at the heart of physical theories.