  We provide necessary and sufficient conditions for when an algebraic stack
admits a good moduli space and prove a semistable reduction theorem for points
of algebraic stacks equipped with a $\Theta$-stratification. These results
provide a generalization of the Keel--Mori theorem to moduli problems whose
objects have positive dimensional automorphism groups and give criteria on the
moduli problem to have a separated or proper good moduli space. To illustrate
our method, we apply these results to construct proper moduli spaces
parameterizing semistable $\mathcal{G}$-bundles on curves and moduli spaces for
objects in abelian categories.
