Two theories revolutionized the 20th century view of space and time: Einstein's general theory of relativity and quantum mechanics. Their union has given rise to elementary particle theories with extra spacetime dimensions, the inflationary model of big bang cosmology, the hypothesis of dark matter in the universe, the discovery of radiation from quantum black holes, and the fuzzy spacetime geometry of superstrings and M-theory. In this work, experts present developments in cosmology, theoretical physics and mathematics, and share their thoughts on the future of spacetime physics.