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Extremely low frequency (ELF) electromagnetic waves have a remarkable ability to propagate with very little attenuation in the earth-ionosphere waveguide. The resulting fields are also able to propagate to moderately great depths in the ocean in spite of the higher conductivity of seawater. The principal drawback in the use of ELF for communication is the inherent inefficiency of the transmitting antenna. Indeed the waves do, however, penetrate to deeply submerged submarines when all other methods fail. This paper presents a tutorial overview on ELF propagation in the earth-ionosphere waveguide. Simple form approximate expressions (relating ELF propagation constants to realistic ionospheric conductivity profiles) are compared with experimentally derived results for both daytime and nighttime propagation conditions. Some anomalous ELF propagation results, along with their probable causes, are also discussed.