  The construction of an averaged theory of gravity based on Einstein's General
Relativity is very difficult due to the non-linear nature of the gravitational
field equations. This problem is further exacerbated by the difficulty in
defining a mathematically precise covariant averaging procedure for tensor
fields over differentiable manifolds. Together, these two ideas have been
called the averaging problem for General Relativity. In the first part of the
talk, an attempt to review some the various approaches to this problem will be
given, highlighting strengths, weaknesses, and commonalities between them. In
the second part of the talk, an argument will be made, that if one wishes to
develop a well-defined averaging procedure, one may choose to parallel
transport along geodesics with respect to the Levi-Cevita connection or, use
the Weitzenb\"ock connection and ensure the transportation is independent of
path. The talk concludes with some open questions to generate further
discussion.
