  We review the properties of the constraint equations, from their geometric
origin in hypersurface geometry through to their roles in the Cauchy problem
and the Hamiltonian formulation of the Einstein equations. We then review
properties of the space of solutions and construction techniques, including the
conformal and conformal thin sandwich methods, the thin sandwich method,
quasi-spherical and generalized QS methods, gluing techniques and the
Corvino-Schoen projection.
