  The motion of sufficiently small body in general relativity should be
accurately described by a geodesic. However, there should be ``gravitational
self-force'' corrections to geodesic motion, analogous to the ``radiation
reaction forces'' that occur in electrodynamics. It is of considerable
importance to be able to calculate these self-force corrections in order to be
able to determine such effects as inspiral motion in the extreme mass ratio
limit. However, severe difficulties arise if one attempts to consider point
particles in the context of general relativity. This article describes these
difficulties and how they have been dealt with.
