This review concerns the current status of the theory of formation of the so-called J-band (Jelley, Scheibe, 1936), an abnormally narrow, high-intensity, red-shifted optical absorption band arising from the aggregation of polymethine dyes. Two opposite approaches to explaining the physical nature of the J-band are given special attention. In the first of these, the old one based on Frenkel’s statistical exciton model, the specific structure of the dye is considered irrelevant, and the J-band is explained by assuming that the quickly moving Frenkel exciton acts to average out the quasistatic disorder in electronic transition energies of molecules in the linear J-aggregate (Knapp, 1984). In the second approach, on the contrary, the specific structure of the dye (the existence of a quasilinear polymethine chain ) is supposed to be very important. This new approach is based on a new theory of charge transfer. The explanation of the J-band here is that an elementary charge transfer along the J-aggregate’s chromophore is dynamically pumped by the chaotic reorganization of nuclei in the nearby environment at a resonance between electronic and nuclear movements — when the motion of nuclei being reorganized is only weakly chaotic (Egorov, 2001).