How well is our universe described by an FLRW model?
  Extremely well! In the $\Lambda$CDM model, the spacetime metric, $g_{ab}$, of
our universe is approximated by an FLRW metric, $g_{ab}^{(0)}$, to about 1 part
in $10^4$ or better on both large and small scales, except in the immediate
vicinity of very strong field objects, such as black holes. However,
derivatives of $g_{ab}$ are not close to derivatives of $g_{ab}^{(0)}$, so
there can be significant differences in the behavior of geodesics and huge
differences in curvature. Consequently, observable quantities in the actual
universe may differ significantly from the corresponding observables in the
FLRW model. Nevertheless, as we shall review here, we have proven general
results showing that---within the framework of our approach to treating
backreaction---the large matter inhomogeneities that occur on small scales
cannot produce significant effects on large scales, so $g_{ab}^{(0)}$ satisfies
Einstein's equation with the averaged stress-energy tensor of matter as its
source. We discuss the flaws in some other approaches that have suggested that
large backreaction effects may occur. As we also will review here, with a
suitable "dictionary," Newtonian cosmologies provide excellent approximations
to cosmological solutions to Einstein's equation (with dust and a cosmological
constant) on all scales. Our results thereby provide strong justification for
the mathematical consistency and validity of the $\Lambda$CDM model within the
context of general relativistic cosmology.
