Electron transfer processes are widespread in biology, chemistry and physics.One of the areas actively studied is the fluorescence and electron transfer in semiconductor nanoparticles, whose size typically varies from 2 to 7 nanometers.The spectrum of the light they emit upon illumination is very narrow and depends markedly on their size.It covers the entire range of the visible spectrum, which is a major advantage in applications, together with their stability.They are readily attached to biological agents, permitting them to serve as biosensors.When they are studied as individual molecules (nanoparticles) under repeated illumination they emit light part of the time, and are dark (no emission) at other times.This intermittency of fluorescence is unusual: instead of the distribution of the "light" periods or dark periods obeying a simple single-exponential probability distribution decay law, their distribution of lifetimes obeys a power law, covering many decades of time.The individual rate processes in these particles span some twelve or more decades of time.The change from a light to a dark state and the reverse is the result of electron transfer processes, the change to the dark state being associated with the formation of a trapped state in or near the surface of the nanoparticle,and the darkness results from a nonradiative process known as an Auger process, which competes with the usual radiative (fluorescent) process.A "detrapping" electron transfer reforms the "light" state.Studies of the phenomena include both "single molecule" and ensemble experiments, which are complementary in the information they provide on the reaction mechanism.We examine and illustrate these studies using the electron transfer theory that has been applied to many other processes in chemistry and biology.