A tutorial review is provided of ultraviolet (UV) and visible radiation transport in the atmosphere-ocean system. Emphasis is placed on the basic physical principles involved, rather than on mathematical/numerical aspects. To illustrate the application of the theory, the effects of an ozone depletion on UV irradiance at the surface are discussed. A comparison of measured and predicted UV penetration into the ocean under the Antarctic ozone hole is also provided. Our ability to model the transport of UV and visible light in the atmosphere-ocean system seems to be limited to a large extent by the lack of information about inherent optical properties of marine constituents, especially in the UV spectral range. To make progress in this area, measurements are needed of spectral absorption and scattering coefficients and volume scattering functions. Identification of the marine constituents that give rise to these optical properties and their variability in space and time is also of crucial importance.