Macromolecular systems comprised of many light-sensitive centres (the photosynthetic unit, dendrimers, and other highly symmetric multichromophore arrays) are important structures offering challenges to theoreticians and synthetic chemists alike. Here we outline novel photophysical interactions predicted and observed in such arrays. Using the tools of molecular quantum electrodynamics (QED) we present quantum amplitudes for a variety of higher-order resonance energy transfer (RET) schemes associated with well-known nonlinear optical effects such as two- and three-photon absorption. The initial analysis is extended to account for situations where the participant donor species are identical and exist in a highly symmetric environment, leading to the possible formation of excitons. It emerges from the QED theory that such excitons are closely associated with the higher-order RET processes. General results are interpreted by analyzing particular molecular architectures which offer interesting features such as rate enhancement or limitation and exciton pathway quenching. Applications in the areas of photosynthesis, molecular logic gates and low-intensity fluorescence energy transfer are predicted.