J-aggregates are fascinating fluorescent nanomaterials formed by highly ordered assembly of organic dyes with the spectroscopic properties dramatically different from that of single or disorderly assembled dye molecules. They demonstrate very narrow red-shifted absorption and emission bands, strongly increased absorbance together with the decrease of radiative lifetime, highly polarized emission and other valuable features. The mechanisms of their electronic transitions are understood by formation of delocalized excitons already on the level of several coupled monomers. Cyanine dyes are unique in forming J-aggregates over the broad spectral range, from blue to near-IR. With the aim to inspire further developments, this review is focused on the optical characteristics of J-aggregates in connection with the dye structures and on their diverse already realized and emerging applications.