  This article summarizes the recent work on the influence of dynamical
tunneling on the control of quantum systems. Specifically, two examples are
discussed. In the first, it is shown that the bichromatic control of tunneling
in a driven double well system is hampered by the phenomenon of chaos-assisted
tunneling. The bichromatic control landscape exhibits several regions
indicating lack of control with every such region involving chaos-assisted
tunneling. The second example illustrates the failure of controlling the
dissociation dynamics of a driven Morse oscillator due to the phenomenon of
resonance-assisted tunneling. In particular, attempts to control the
dissociation dynamics by rebuilding local phase space barriers are foiled due
to resonance-assisted tunneling.
