We review recent progress on holographic renormalization in the context of the gauge-gravity correspondence when the bulk geometry is not asymptotically AdS. The prime example is the Klebanov-Strassler background, whose dual gauge theory has logarithmically running couplings at all energy scales. The presented formalism provides the counterterms necessary for obtaining finite two-point functions of the scalar operators in the corresponding dual gauge theories. The presentation is self-contained and reviews all the relevant background material concerning a gauge-invariant description of the fluctuations around holographic renormalization group backgrounds.