Varying speed of light, cosmic structure and the quest for quantum gravity

Varying constants theories in several guises may be essential for the resolution of a number of impasses in cosmology and quantum gravity. Perhaps the most radical of them all — varying speed of light theories — may be the clue to extracting phenomenology from quantum gravity theories, finally rendering the field properly a branch of science. I will review this possibility, with particular emphasis on the issue of the generation of cosmic structure and primordial gravitational waves.