Resonance energy transfer (RET) is a process that permits the directed flow of optical energy through systems comprised of multiple chromophores, the most familiar example of which being the transfer of energy in photosynthetic light harvesting complexes. This non-radiative energy transfer mechanism occurs when the oscillating transition dipole moment of a donor species, initially excited by an external electromagnetic field, exerts a potential that induces a second oscillating transition dipole moment in a nearby acceptor species. The strength of this potential, and therefore the RET rate, depends on the magnitudes, relative orientation, and spatial proximity of the donor and acceptor transition dipole moments, as well as on the overlap in the frequency of the dipole oscillations. Generally speaking, large RET rates require large overlap between the donor and acceptor dipole moments and frequencies, and donor-acceptor separations of a few nanometers or less. The sensitivity of the RET rate to these parameters has led to the development of RET as a probe for the nanoscale structure of complex molecular and biomolecular systems. Substantial effort has recently been focused on the development of nanoscale systems with RET donor and acceptor components that are capable of highly-efficient and selective transfer of optical energy. Common features of the donors and acceptors in such engineered systems include strong intrinsic optical resonances. The large transition dipole moments and tunable excitation energies associated with quantum dots (QD) and semiconductor nanoplatlets make them promising candidates as efficient RET donors and acceptors. Similarly, engineered molecular systems, including J-aggregates and QD-J-Aggregate hybrids have been studied as platforms for nanoscale RET. Plasmonic resonances also tend to display large transition dipoles, so noble metal nanoparticles form another class of potential RET donors to molecules, semi-conductors, and to other plasmonic nanoparticles. However, the competition between energy transfer and relaxation events becomes particularly important for determining the efficacy of RET in plasmonic systems.