The rotational frequency shift (RFS) has been investigated. The existence of the RFS, previously proposed [Phys. Rev. Lett., 78, 2539 (1997)], has been explicitly demonstrated experimentally for the first time, for different quantum systems and frequency regimes. Suitable laser spectroscopical experiments have been designed, and performed with atomic and molecular quantum systems. The fast rotation-RFS has been verified for atomic lithium. In this experiment, the electric field of a circularly polarized strong laser beam has been employed as the rotating environment. The spectra have been analyzed first using the concept of the dynamic Stark effect, and then using that of the rotational frequency shift. The most interesting intermediate-RFS case has been demonstrated with the aid of the thioformaldehyde molecule which was exposed to a rotating radio frequency electric field. The existence of the strong field-RFS has been shown by reanalyzing an already existing experiment [Phys. Rev. Lett., 58, 2281 (1987)]. Finally, the relation between the strong field-RFS and the Berry phase has been discussed, and the dressed state method, the fictitious magnetic field, and the Sagnac effect have been considered in the light of the rotational frequency shift theory.