In pursuit of a better understanding of how electronic excitation migrates within complex structures, the concept of resonance energy transfer is being extended and deployed in a wide range of applications. Utilizing knowledge of the quantum interactions that operate in natural photosynthetic systems, wide-ranging molecular and solid-state materials are explored in the cause of more efficient solar energy harvesting, while advances in theory are paving the way for the development and application of fundamentally new mechanisms. In this review, an introduction to the underlying processes that cause singlet-singlet and triplet-triplet energy transfer leads into a discussion of how a new conception of these fundamental processes has emerged over recent years. Illustrative examples relevant to laser science and photonics are described, including photosynthetic light-harvesting, light-activated sensors, processes of cooperative and accretive energy pooling and quantum cutting in rare earth-doped crystals, and incoherent triplet-triplet energy upconversion in molecular solutions.