Energy transport during chemical reactions or following photoexcitation in systems of biological molecules is mediated by numerous interfaces that separate chemical groups and molecules. Describing and predicting energy transport has been complicated by the inhomogeneous environment through which it occurs, and general rules are still lacking. We discuss recent work on identification of networks for vibrational energy transport in biomolecules and their environment, with focus on the nature of energy transfer across interfaces. Energy transport is influenced both by structure of the biomolecular system as well as by equilibrium fluctuations of nonbonded contacts between chemical groups, biomolecules, and water along the network. We also discuss recent theoretical and computational work on the related topic of thermal transport through molecular interfaces, with focus on systems important in biology as well as relevant experimental studies.