  Liouville quantum gravity (LQG) is a one-parameter family of models of random
fractal surfaces which first appeared in the physics literature in the 1980s.
Recent works have constructed a metric (distance function) on an LQG surface.
We give an overview of the construction of this metric and discuss some of its
most important properties, such as the behavior of geodesics and the KPZ
formula. We also discuss some of the main techniques for proving statements
about the LQG metric, give examples of their use, and discuss some open
problems.
