  We discuss various Penrose limits of conformal and nonconformal backgrounds.
In AdS_5 x T^{1,1}, for a particular choice of the angular coordinate in
T^{1,1} the resulting Penrose limit coincides with the similar limit for AdS_5
x S^5. In this case an identification of a subset of field theory operators
with the string zero modes creation operators is possible. For another limit we
obtain a light-cone string action that resembles a particle in a magnetic
field. We also consider three different types of backgrounds that are dual to
nonconformal field theories: The Schwarzschild black hole in AdS_5, D3-branes
on the small resolution of the conifold and the Klebanov-Tseytlin background.
We find that in all three cases the introduction of nonconformality renders a
theory that is no longer exactly solvable and that the form of the deformation
is universal. The corresponding world sheet theory in the light-cone gauge has
a \tau=x^+ dependent mass term.
