  In general relativity (GR), spacetime geometry is no longer just a background
arena but a physical and dynamical entity with its own degrees of freedom. We
present an overview of approaches to quantum gravity in which this central
feature of GR is at the forefront. However, the short distance dynamics in the
quantum theory are quite different from those of GR and classical spacetimes
and gravitons emerge only in a suitable limit. Our emphasis is on communicating
the key strategies, the main results and open issues. In the spirit of this
volume, we focus on a few avenues that have led to the most significant
advances over the past 2-3 decades.
