The greatest challenge in fundamental physics attempts to reconcile quantum mechanics and general relativity in a theory of quantum gravity. The project suggests a profound revision of the notions of space, time and matter. It has become a key topic of debate and collaboration between physicists and philosophers. This volume collects classic and original contributions from leading experts in both fields for a provocative discussion of the issues. It contains accessible introductions to the main and less-well-known known approaches to quantum gravity. It includes exciting topics such as the fate of spacetime in various theories, the so-called problem of time in canonical quantum gravity, black hole thermodynamics, and the relationship between the interpretation of quantum theory and quantum gravity. This book will be essential reading for anyone interested in the profound implications of trying to marry the two most important theories in physics.