  General relativity becomes vastly simpler in three spacetime dimensions: all
vacuum solutions have constant curvature, and the moduli space of solutions can
be almost completely characterized. As a result, this lower dimensional setting
becomes an ideal test bed for a wide range of approaches to quantum gravity,
from reduced phase phase space quantization to covariant canonical quantization
to path integral methods to asymptotic quantization of "edge states." Here I
review a variety of classical descriptions of the moduli space of solutions and
a broad range of quantizations, with special attention to implications for
realistic quantum gravity in four spacetime dimensions.
