  Let $\mathcal{K}(n, V)$ be the set of $n$-dimensional compact Kahler-Einstein
manifolds $(X, g)$ satisfying $Ric(g)= - g$ with volume bounded above by $V$.
We prove that after passing to a subsequence, any sequence $\{ (X_j,
g_j)\}_{j=1}^\infty$ in $\mathcal{K}(n, V)$ converges, in the pointed
Gromov-Hausdorff topology, to a finite union of complete Kahler-Einstein metric
spaces without loss of volume. The convergence is smooth off a closed singular
set of Hausdorff dimension no greater than $2n-4$, and the limiting metric
space is biholomorphic to an $n$-dimensional semi-log canonical model with its
non log terminal locus of complex dimension no greater than $n-1$ removed. We
also show that the Weil-Petersson metric extends uniquely to a Kahler current
with bounded local potentials on the KSBA compactification of the moduli space
of canonically polarized manifolds. In particular, the coarse KSBA moduli space
has finite volume with respect to the Weil-Petersson metric. Our results are a
high dimensional generalization of the well known compactness results for
hyperbolic metrics on compact Riemann surfaces of fixed genus greater than one.
