In the last decade we have been witness to striking advances in our understanding of the mechanism of resonance and chaos assisted tunneling in a variety of systems. However, majority of the systems studied have two or fewer degrees of freedom. It is well known, for more than a few decades now, that systems with three or more degrees of freedom represent the ``final frontier" in terms of understanding the nature of the phase space structures and their influence on classical transport. Are the proposed dynamical tunneling mechanisms valid in such systems? Is it conceivable that novel phase space transport mechanisms such as ``Arnold diffusion" might mask typical signatures of dynamical tunneling? In this talk I intend to use certain examples to try and highlight, and perhaps even understand, some of the key issues.