  The Deligne-Mumford stable reduction theorem asserts that for a family of
stable curves over the punctured disk, after a finite base change, the family
can be completed in a unique way to a family of stable curves over the disk. In
this survey we discuss stable reduction theorems in a number of different
contexts. This includes a review of recent results on abelian varieties,
canonically polarized varieties, and singularities. We also consider the
semi-stable reduction theorem and results concerning simultaneous stable
reduction.
