The physics and mathematics of how radiation passes through a medium that may contain any combination of scatterers, absorbers, and emitters. In meteorology, the study of radiative transfer dates back at least to Lord Rayleigh's investigations in 1871 on the nature of scattering by air molecules. Since that time, sophisticated mathematical solutions to radiative transfer have been developed, especially for one-dimensional monochromatic problems. The more general problem of solving broadband radiative transfer in three-dimensional cloudy atmospheres requires a computational solution.