In the supergravity approximation of the AdS/CFT correspondence correlation fucntions of the strongly coupled gauge theory can be computed by evaluating the on-shell supergravity action with arbitrary Dirichlet boundary conditions for the various fields. It is well known, however, that the on-shell action on the conformal boundary of AdS diverges due to the infinite volume of the bulk. Holographic Renormalization is a method for systematically constructing covariant counter terms which remove the divergences of the on-shell supergravity action for any asymptotically AdS space and it provides an algorithm for calculating renormalized correlation functions of the strongly coupled gauge theory. I will review the main steps involved in this algorithm and present a recently developed Hamiltonian version of the method where the AdS radius plays the role of time in the Hamiltonian formalism. I will then apply this method to calculate correlation functions in the field theory duals of various Poincare and AdS-sliced domain wall solutions of five dimensional gauged supergravity, including the recently discovered Janus background.