In 1970, three laboratories independently made a discovery that, for aromatic fluorophores embedded into different rigid and highly viscous media, the spectroscopic properties do not conform to classical rules. The fluorescence spectra can depend on excitation wavelength, and the excited-state energy transfer, if present, fails at the "red" excitation edge. These red-edge effects were related to the existence of excited-state distribution of fluorophores on their interaction energy with the environment and the slow rate of dielectric relaxation of this environment. In these conditions the site-selection can be provided by variation of the energy of illuminating light quanta, and the behaviour of selected species can be followed as a function of time and other variables. These observations found extensive application in different areas of research: colloid and polymer science, molecular biophysics, photochemistry and photobiology. In particular, they led to the development of very productive methods of studying the dynamics of dielectric relaxations in protein and membranes, using the tryptophan emission and the emission of a variety of probes. These studies were extended to the time domain with the observation of new site-selective effects in emission intensity and anisotropy decays. They stimulated the emergence and development of cryogenic energy-selective and single-molecular techniques that became valuable tools in their own right in chemistry and biophysics research. Site-selection effects were discovered for electron-transfer and proton-transfer reactions if they depended on the dynamics of the environment. This review is focused on the progress in the field of red-edge effects, their applications and prospects.