Initial data are the starting point for any numerical simulation. In the case
of numerical relativity, Einstein's equations constrain our choices of these
initial data. We will examine several of the formalisms used for specifying
Cauchy initial data in the 3+1 decomposition of Einstein's equations. We will
then explore how these formalisms have been used in constructing initial data
for spacetimes containing black holes and neutron stars. In the topics
discussed, emphasis is placed on those issues that are important for obtaining
astrophysically realistic initial data for compact binary coalescence.Comment: 50 pages, LaTeX(livrev.cls), Review article for "Living Reviews in
Relativity" (http://www.livingreviews.org/), July 200
