  In this paper we consider both Abelian as well as non-Abelian T-duals of the
Klebanov-Witten background and inspect their various Penrose limits. We show
that these backgrounds admit pp-wave solutions in the neighbourhood of
appropriate null geodesics. We study the quantization of closed string
propagating on some of the resulting pp-wave backgrounds and comment on the
probable field theory duals.
