Vistas in numerical relativity

Upcoming gravitational wave-experiments promise a window for discovering new physics in astronomy. Detection sensitivity of the broadband laser interferometric detectors LIGO/VIRGO may be enhanced by matched filtering with accurate wave-form templates. Where analytic methods break down, we have to resort to numerical relativity, often in Hamiltonian or various hyperbolic formulations. Well-posed numerical relativity requires consistency with the elliptic constraints of energy and momentum conservation. We explore this using a choice of gauge in the future and a dynamical gauge in the past. Applied to a polarized Gowdy wave, this enables solving {\em all} ten vacuum Einstein equations. Evolution of the Schwarzschild metric in 3+1 and, more generally, sufficient conditions for well-posed numerical relativity continue to be open challenges.