  Herein we present open problems and survey examples and theorems concerning
sequences of Riemannian manifolds with uniform lower bounds on scalar curvature
and their limit spaces. Examples of Gromov and of Ilmanen which naturally ought
to have certain limit spaces do not converge with respect to smooth or
Gromov-Hausdorff convergence. Thus we focus here on the notion of Intrinsic
Flat convergence, developed jointly with Wenger. This notion has been applied
successfully to study sequences that arise in General Relativity. Gromov has
suggested it should be applied in other settings as well. We first review
intrinsic flat convergence, its properties, and its compactness theorems,
before presenting the applications and the open problems.
