  We systematically develop the procedure of holographic renormalization for RG
flows dual to asymptotically AdS domain walls. All divergences of the on-shell
bulk action can be cancelled by adding covariant local boundary counterterms
determined by the near-boundary behavior of bulk fields. This procedure defines
a renormalized action from which correlation functions are obtained by
functional differentiation. The correlators are finite and well behaved at
coincident points. Ward identities, corrected for anomalies, are satisfied. The
correlators depend on parts of the solution of the bulk field equations which
are not determined by near-boundary analysis. In principle a full nonlinear
solution is required, but one can solve linearized fluctuation equations to
define a bulk-to-boundary propagator from which 2-point correlation functions
are easily obtained. We carry out the procedure explicitly for two known RG
flows obtained from the maximal gauged D=5 supergravity theory, obtaining new
results on correlators of vector currents and related scalar operators and
giving further details on a recent analysis of the stress tensor sector.
