Abstract The different kinds of excitons are considered taking into account the electron-electron interaction as well as the electron-lattice interaction. Some earlier results published by T oyozawa, H eller and M arcus are obtained as special cases. A refined theory of dielectric screening due to lattice vibrations is given. Optical properties of excitons with large orbital radii are discussed. Certain selection rules as well as a possible explanation of dichroitic effects are given and compared with the corresponding ones of impurity atoms. Finally a quantitative theory of the elementary process of energy transfer by excitons is given and compared with the resonance energy transfer process investigated by Dexter.