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This paper presents a review of basic theories and recent advances in the studies of wave propagation and scattering in random media. Examples of the random media include the atmosphere, the ocean, and biological media whose characteristics are randomly varying in time and space. The study of electromagnetic, optical, and acoustic waves in such media has become increasingly important in recent years in the areas of communication, detection, and remote-sensing. Topics covered in this paper are divided into "waves in randomly distributed scatterers," "waves in random continua," and "remote-sensing of random media." Transport theory with various approximate solutions and multiple scattering theories are discussed and their relationships are clarified. Included in the analyses are propagation characteristics of intensities, wave fluctuations, pulse propagation and scattering, coherence bandwidth, and coherence time of communication channels through random media. Remote-sensing techniques include recent advances in the use of inversion techniques to deal with ill-posed problems.