  After motivating why the study of asymptotically flat spaces is important in
loop quantum gravity, we review the extension of the standard framework of this
theory to the asymptotically flat sector based on the GNS construction. In
particular, we provide a general procedure for constructing new Hilbert spaces
for loop quantum gravity on non-compact spatial manifolds. States in these
Hilbert spaces can be interpreted as describing fluctuations around fiducial
fixed backgrounds. When the backgrounds are chosen to approximate classical
asymptotically flat 3-geometries this gives a natural framework in which to
discuss physical applications of loop quantum gravity, especially its
semi-classical limit. We present three general proposals for the construction
of suitable backgrounds, including one approach that can lead to quantum
gravity on anti-DeSitter space as described by the Chern-Simons state.
