Interactions between excited molecules will prevail in organic crystals or aggregates, provided that the absorption coefficient of the component molecule is high and they are arranged periodically. This phenomenon is called excitonic interactions(i.e. interactions between transition dipoles) observed often in dyestuffs and pigments that induces spectral shifts or band splitting(Davydov splitting). The present paper describes an overview of the exciton theory and presents some examples which include J-aggregates of cyanine dyestuffs.