  The conformal method for constructing initial data for Einstein's equations
is presented in both the Hamiltonian and Lagrangian picture (extrinsic
curvature decomposition and conformal thin sandwich formalism, respectively),
and advantages due to the recent introduction of a weight-function in the
extrinsic curvature decomposition are discussed. I then describe recent
progress in numerical techniques to solve the resulting elliptic equations, and
explore innovative approaches toward the construction of astrophysically
realistic initial data for binary black hole simulations.
