  This is a survey article about Siegel modular varieties over the complex
numbers. It is written mostly from the point of view of moduli of abelian
varieties, especially surfaces. We cover compactification of Siegel modular
varieties; classification of the compactified varieties by Kodaira dimension,
etc.; moduli of abelian surfaces and especially applications of the lifting of
Jacobi forms to modular forms; projective models of some special Siegel modular
3-folds; non-principally polarized abelian surfaces; and constructing
degenerating families of abelian varieties.
