This review is devoted to ultra-low-frequency electromagnetic waves of a natural origin. A variety of frequency-modulated waves whose sources are located in the ionosphere, in the radiation belt, on the periphery of the magnetosphere, and in the solar wind in front of the magnetosphere bow shock are considered. The main focus is on the mechanisms of the formation of frequency modulation. Analysis of frequency modulation gives us information about the processes of excitation and propagation of waves, as well as about physical conditions in places of excitation and along signal propagation paths. Relevant open question about the physics of frequency-modulated waves are indicated.