  A review of the treatment of boundaries in general relativity is presented
with the emphasis on application to the formulations of Einstein's equations
used in numerical relativity. At present, it is known how to treat boundaries
in the harmonic formulation of Einstein's equations and a tetrad formulation of
the Einstein-Bianchi system. However, a universal approach valid for other
formulations is not in hand. In particular, there is no satisfactory boundary
theory for the 3+1 formulations which have been highly successful in binary
black hole simulation. I discuss the underlying problems that make the
initial-boundary value problem much more complicated than the Cauchy problem. I
review the progress that has been made and the important open questions that
remain.
