  Intramolecular vibrational energy redistribution (IVR) impacts the dynamics
of reactions in a profound way. Theoretical and experimental studies are
increasingly indicating that accounting for the finite rate of energy flow is
critical for uncovering the correct reaction mechanisms and calculating
accurate rates. This requires an explicit understanding of the influence and
interplay of the various anharmonic (Fermi) resonances that lead to the
coupling of the vibrational modes. In this regard, the local random matrix
theory (LRMT) and the related Bose-statistics triangle rule (BSTR) model have
emerged as a powerful and predictive quantum theories for IVR. In this
Perspective we highlight the close correspondence between LRMT and the
classical phase space perspective on IVR, primarily using model Hamiltonians
with three degrees of freedom. Our purpose for this is threefold. First, this
clearly brings out the extent to which IVR pathways are essentially classical,
and hence crucial towards attempts to control IVR. Second, given that LRMT and
BSTR are designed to be applicable for large molecules, the exquisite
correspondence observed even for small molecules allows for insights into the
quantum ergodicity transition. Third, we showcase the power of modern nonlinear
dynamics methods in analysing high dimensional phase spaces, thereby extending
the deep insights into IVR that were earlier gained for systems with
effectively two degrees of freedom. We begin with a brief overview of recent
examples where IVR plays an important role and conclude by mentioning the
outstanding problems and the potential connections to issues of interest in
other fields.
