Over the preceeding twenty years, the role of underlying classical dynamics
in quantum mechanical tunneling has received considerable attention. A num
ber of new tunneling phenomena have been uncovered that have been directly
linked to the set of dynamical possibilities arising in simple systems that
contain at least some chaotic motion. These tunneling phenomena can be ide
ntified by their novel h-dependencies and/or statistical behaviors. We summ
arize a sampling of these phenomena and mention some applications.