  We study gravitational aspects of Brane-World scenarios. We show that the
bulk Einstein equations together with the junction condition imply that the
induced metric on the brane satisfies the full non-linear Einstein equations
with a specific effective stress energy tensor. This result holds for any value
of the bulk cosmological constant. The analysis is done by either placing the
brane close to infinity or by considering the local geometry near the brane. In
the case that the bulk spacetime is asymptotically AdS, we show that the
effective stress energy tensor is equal to the sum of the stress energy tensor
of matter localized on the brane and of the holographic stress energy tensor
appearing in the AdS/CFT duality. In addition, there are specific
higher-curvature corrections to Einstein's equations. We analyze in detail the
case of asymptotically flat spacetime. We obtain asymptotic solutions of
Einstein's equations and show that the effective Newton's constant on the brane
depends on the position of the brane.
