This article reviews some recent work in molecular vibrational energy flow (IVR), with emphasis on our own computational and experimental studies. We consider the problem in various representations, and use these to develop a family of simple models which combine specific molecular properties (e.g. size, vibrational frequencies) with statistical properties of the potential energy surface and wavefunctions. This marriage of molecular detail and statistical simplification captures trends of IVR mechanisms and survival probabilities beyond the abilities of purely statistical models or the computational limitations of full ab initio approaches. Of particular interest is IVR in the intermediate time regime, where heavy-atom skeletal modes take over the IVR process from hydrogenic motions even upon X H bond excitation. Experiments and calculations on prototype heavy-atom systems show that intermediate time IVR differs in many aspects from the early stages of hydrogenic mode IVR. As a result, IVR can be coherently frozen, with potential applications to selective chemistry.