Fluorescence resonance energy transfer (FRET) is a popular tool to study equilibrium and dynamical properties of polymers and biopolymers in condensed phases and is now widely used in conjunction with single molecule spectroscopy. In the data analysis, one usually employs the Förster expression which predicts (l/R⁶) distance dependence of the energy transfer rate. However, critical analysis shows that this e_xpression can be of rather limited validity in many cases. We demonstrate this by explicitly considering a donor-acceptor system, polyfluorene (PF₆)-tetraphenylporphyrin (TPP), where the size of both donor and acceptor is comparable to the distance separating them. In such cases, one may expect much weaker distance (as l/R² or even weaker) dependence. We have also considered the case of energy transfer from a dye to a nanoparticle. Here we find l/R⁴ distance dependence at large separations, completely different from Förster. We also discuss recent application of FRET to study polymer conformational dynamics.